Motion along a Straight Line

Figure 2-1 6 gives the velocity of a particle moving on an x axis. What

are (a) the initial and (b) the final directions of travel? (c) Does the particle stop momentarily? (d) Is the acceleration positive or negative? (e) Is it constant or varying?

Figure 2-17 gives the acceleration a(t) of a Chihuahua as it chases a German shepherd along an axis. In which of the time periods indicated does the Chihuahua move at constant speed?

Figure 2-18 shows four paths along which objects move from a starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines. Rank the paths according to (a) the average velocity of the objects and (b) the average speed of the objects, greatest

first.

Figure 2-19 is a graph of a particle’s position along an x axis versus time. (a) At time$\mathit{t}\mathbf{=}\mathbf{0}$, what is the sign of the particle’s position? Is the particle’s velocity positive, negative, or 0 at (b)$\mathit{t}\mathbf{=}\mathbf{1}\mathbf{ }\mathit{s}$, (c)$\mathit{t}\mathbf{=}\mathbf{2}\mathbf{ }\mathbf{s}$, and (d)$\mathit{t}\mathbf{=}\mathbf{3}\mathbf{ }\mathbf{s}$? (e) How many times does the particle go through the point$\mathbf{x}\mathbf{=}\mathbf{0}$?

 Figure 2-20 gives the velocity of a particle moving along an axis. Point 1 is at the highest point on the curve; point 4 is at the lowest point; and points 2 and 6 are at the same height. What is the direction of travel at (a) time $\mathbf{t}\mathbf{=}\mathbf{0}$and (b) point 4? (c) At which of the six numbered points does the particle reverse its direction of travel? (d) Rank the six points according to the magnitude of the acceleration, greatest first.

At , a particle moving along an x axis is at position . The signs of particle’s initial velocity  (at time ) and constant acceleration a are, respectively, for four situations$\mathbf{-}\left(1\right)\mathbf{+}\mathbf{,}\mathbf{+}\left(2\right)\mathbf{+}\mathbf{,}\mathbf{-}\left(3\right)\mathbf{-}\mathbf{,}\mathbf{+}\left(4\right)\mathbf{-}\mathbf{,}\mathbf{-}$ In which situations will the particle (a) stop momentarily, (b) pass through the origin, and (c) never pass through the origin?

Hanging over the railing of a bridge, you drop an egg (no initial velocity) as you throw a second egg downward. Which curves in Fig 2-21 give the velocity  for- (a) the dropped egg and (b) the thrown egg? (Curves A and B are parallel, so are C, D and E, so are F and G)

Question: While driving a car at 90 km/hr , how far do you move while your eyes shut for  during a hard sneeze?

Question: Compute your average velocity in following two cases: (a) You walk 73.2 m at a speed of 1.22 m/s  and then run 73.2 at a speed of 3.05m/s along a straight track. (b) You walk for1 min  at a speed of 1.22m/s  and then run for1 min at  3.05m/s  along a straight track. (c) Graph x versus t for both cases and indicate how the average velocity is found on the graph.

Question: An automobile travels on a straight road for 40 km at 30 km/hr. It then continues in same direction for another  40 km at 60 km/hr. (a) What is the average velocity of car during the full 80 km trip? (Assume that it moves in positive x direction) (b) What is the average speed? (c) Graph x versus t and indicate how the average velocity is found on the graph.

Question: A car moves uphill at 40 km/hand then back downhill at 60 km/h . What is the average speed for the round trip?

The position of an object moving along an x axis is given by ,$x=3t-4t^2+t^3$ where x is in metres and t in seconds. Find the position of the object at following values of t: a) 1sec ,(b) 2sec, (c) 3sec, and (d) 4sec, (e) What is the object’s displacement between t=0 and t=4sec ? (f) What is its average velocity for the time interval from t=2s to t=4s? (g) Graph x vs t for $0\le t\le 4 sec$  and indicate how the answer for f can be found on the graph.

The 1992 world speed record for a bicycle (human powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 sec , at which he commented “Cogito ergo zoom!” (I think, therefore I go fast). In 2001, Sam Whittingham beat Huber’s record by 19.0 km/h. What was Whittingham’s time through the 200 m?

Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h  flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train, the bird flies directly back to the first train and so forth. (We have no idea why a bird would behave in this way). What is the total distance the bird travels before the trains collide?

Figure shows a general situation in which a stream of people attempts to escape through an exit door that turns out to be locked. The people move toward the door at speed $V_s=3.5 m/s$ , are each d=0.25 m in depth, and are separated by L=1.75 m. The arrangement in figure 2-24 occurs at time t=0 . (a) At what average rate does the layer of people at door increase? (b) At what time does the layer’s depth reach 5 m? (The answers reveal how quickly such a situation becomes dangerous)

                       Figure 2-24 Problem 8

The following equations give the velocity  of a particle in four situations: $\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathit{v}\mathbf{=}\mathbf{3}\mathbf{ }\mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathit{v}\mathbf{=}\mathbf{4}{\mathit{t}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{t}\mathbf{-}\mathbf{6}\mathbf{ }\mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathit{v}\mathbf{=}\mathbf{3}\mathit{t}\mathbf{-}\mathbf{4}\mathbf{ }\mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathit{v}\mathbf{=}\mathbf{5}{\mathit{t}}^{\mathbf{2}}\mathbf{-}\mathbf{3}$ .To which of these situations do the equations of Table 2-1 apply?

In  races, runner 1 on track 1 (with time $\mathbf{2}\mathbf{ }\mathbf{min}\mathbf{,}\mathbf{ }\mathbf{27}\mathbf{.}\mathbf{95}\mathbf{ }\mathbf{sec}$ ) appears to be faster than runner 2 on track 2 ($\mathbf{2}\mathbf{ }\mathbf{min}\mathbf{,}\mathbf{ }\mathbf{28}\mathbf{.}\mathbf{15}\mathbf{ }\mathbf{sec}$). However, length $L_2$  of track 2 might be slightly greater than length $L_1$ of track 1. How large $L_2-L_1$can  be for us still to conclude that runner 1 is faster?

In Fig 2-22, a cream tangerine is thrown directly upward past three evenly spaced windows of equal heights. Rank the windows according to (a) the average speed of the cream tangerine while passing them (b) the time the cream tangerine takes to pass them, (c) the magnitude of the acceleration of cream tangerine while passing them and (d) the change in the speed of cream tangerine during the passage, greatest first.

Suppose that a passenger intent on lunch during his first ride in a hot-air balloon accidently drops an apple over the side during the balloon’s liftoff. At the moment of the apple’s release, the balloon is accelerating upward with a magnitude of $\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ and has an upward velocity of 2 m / s magnitude . What are the (a) magnitude and (b) direction of the acceleration of the apple just after it is released? (c) Just then, is the apple moving upward or downward, or is it stationery? (d) What is the magnitude of its velocity just then? (e) In the next few moments, does the speed of the apple increase, decrease, or remain constant?

To set a speed record in a measured (straight line) distance d, a race car must be driven in one direction (in time $t_1$ ) and then in the opposite direction (in time $t_2$ ). (a) To eliminate the effects of wind and obtain the car’s speed in a windless situation, should we find the average of $\raisebox{1ex}{$d$}\!\left/ \!\raisebox{-1ex}{$$}\right.t_1$ and $\raisebox{1ex}{$d$}\!\left/ \!\raisebox{-1ex}{$t_2$}\right.$ (method 1) or should we divide d  by the average of $t_1$ and $t_2$? (b) What is the fractional difference in the two methods when a steady wind blows along the car’s route and the ratio of wind speed $V_w$  to car’s speed $V_c$  is 0.0240.

You are to drive 300km to an interview. The interview is at 11.15 AM. You plan to drive at 100 km/h , so you leave at 8 AM, to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40km. What would be the least speed needed for the rest of the trip to arrive in time for the interview?

An abrupt slowdown in concentrated traffic can travel as a pulse, termed a shock wave, along the line of cars, either downstream (in traffic direction) or upstream, or it can be stationary. Figure 2-25 shows a uniformly spaced line of cars moving at speed V=25 m/s toward a uniformly spaced line of slow cars moving at speed${\mathit{v}}_{\mathbf{s}}\mathbf{=}\mathbf{5}\mathit{m}\mathbf{/}\mathit{s}$. Assume that each faster car adds length L=12.0 m (car length plus buffer zone) to the line of slow cars when it joins the line, and assume it slows abruptly at the last instant.  (a) For what separation distance d between the faster cars does the shock wave remain stationary? If the separation is twice the amount, (b) What is the Speed? (c) What is the Direction (upstream or downstream) of the shock wave?

You drive on Interstate 10 from San Antonio to Houston, half the time at $\mathbf{55}\mathbf{km}\mathbf{/}\mathbf{h}$and other half at$\mathbf{90}\mathbf{km}\mathbf{/}\mathbf{h}$. What is your average speed (a) from San Antonio to Houston? (b) from Houston back to San Antonio? (c) for the entire trip? (d) What is your average velocity for the entire trip? (e) Sketch x vs t for (a), assuming the motion is all in positive x direction. Indicate how the average velocity can be found on the sketch.

An electron moving along the x axis has a position given by $\mathit{x}\mathbf{=}\mathbf{16}{\mathit{e}}^{\mathbf{-}\mathbf{t}}$, where t is in seconds. How far is the electron from the origin when it momentarily stops?

(a) If a particle’s position is given by $\mathbf{x}\mathbf{=}\mathbf{4}\mathbf{-}\mathbf{12}\mathbf{t}\mathbf{+}\mathbf{3}{\mathbf{t}}^{\mathbf{2}}$ (where t is in sec and x in metres), what is its velocity at $\mathbf{t}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{sec}$ ? (b) Is it moving in positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculations) (e) Is there ever an instant when the velocity is zero? If so, give the time t, if no, answer no. (f) Is there a time after $\mathbf{t}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{3}\mathbf{ }\mathbf{sec}$ when the particle is moving in negative direction of x? If so, give the time t, if no, answer no.

The position function $\mathbf{x}\mathbf{\left(}\mathbf{t}\mathbf{\right)}$ of a particle moving along an x axis is $\mathbf{x}\mathbf{=}\mathbf{4}\mathbf{-}\mathbf{6}{\mathbf{t}}^{\mathbf{2}}$ , with x in metres and t in seconds. (a) At what time does the particle momentarily stop? (b) Where does the particle momentarily stop? At what (c) negative time and (d) positive time does the particle pass through the origin? (e) Graph x vs t for range $\mathbf{-}\mathbf{5}\mathbf{ }\mathbf{sec}$   to $\mathbf{+}\mathbf{5}\mathbf{ }\mathbf{sec}$. (f) To shift the curve rightward on the graph, should we include the term   $\mathbf{+}\mathbf{20}\mathbf{t}$ or $\mathbf{-}\mathbf{20}\mathbf{t}$ in ? (g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

The position function x(t) of a particle moving along an x axis is $\mathbf{x}\mathbf{=}\mathbf{4}\mathbf{-}\mathbf{6}{\mathbf{t}}^{\mathbf{2}}$, with x in metres and t in seconds. (a) At what time does the particle momentarily stop? (b) Where does the particle momentarily stop? At what (c) negative time and (d) positive time does the particle pass through the origin? (e) Graph x vs t for range -5 sec to +5 sec. (f) To shift the curve rightward on the graph, should we include the term +20t or -20t in x(t)? (g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

The position of a particle moving along x axis is given in cm by $\mathbf{x}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{75}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{50}{\mathbf{t}}^{\mathbf{3}}$, where t is in seconds. Calculate (a) the average velocity during time interval t=2 s to t=3 s; (b) the instantaneous velocity at t=2 s; (c) the instantaneous velocity at t=3s; (d) the instantaneous velocity at t=2.5 s; (e) the instantaneous velocity when the particle is midway between its positions at t=2 s and t=3 s (f) Graph x vs. t and indicate your answers graphically.

The position of a particle moving along an x axis is given by $\mathbf{x}\mathbf{=}\mathbf{12}{\mathbf{t}}^{\mathbf{2}}\mathbf{-}\mathbf{2}{\mathbf{t}}^{\mathbf{3}}$, where x in metres and t in sec. Determine (a) the position. (b) the velocity, and (c) the acceleration of the particle at t=3 s . (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle, and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving? (Other than t=0)? (i) Determine the average velocity of the particle between t=0 and t=3 s . 

At a certain time, a particle had a speed of$\mathbf{18}\mathbf{m}\mathbf{/}\mathbf{s}$ in positive x direction, and 2.4 s later, its speed was 30 m/s in the opposite direction. What is the average acceleration of particle during this 2.4 s interval?

(a) If the position of a particle is given by $\mathbf{x}\mathbf{=}\mathbf{20}\mathbf{t}\mathbf{-}\mathbf{5}{\mathbf{t}}^{\mathbf{2}}$, where x is in m and t in sec when, if ever, the particle’s velocity is zero? (b) When is its acceleration a zero? (c) For what time range (positive or negative) is a negative? (d) Positive? (e) Graph x(t), v(t) and a(t).

From t=0 to $\mathbf{t}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{min}$, a man stands still, and from  $\mathbf{t}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{min}$to$\mathbf{t}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{min}$ , he walks briskly in a straight line at a constant speed of $\mathbf{2}\mathbf{.}\mathbf{20}\mathbf{m}\mathbf{/}\mathbf{s}$. What are a) his average velocity  ${\mathbf{V}}_{\mathbf{avg}}$b) his average acceleration ${\mathbf{a}}_{\mathbf{avg}}$in time interval $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{min}$ to$\mathbf{8}\mathbf{.}\mathbf{00}\mathbf{min}$ ? What are c) ${\mathbf{V}}_{\mathbf{avg}}$d) ${\mathbf{a}}_{\mathbf{avg}}$in time interval $\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{min}$ to $\mathbf{9}\mathbf{.}\mathbf{00}\mathbf{min}$? e) Sketch x vs t and v vs t and indicate how the answers of (a) through (d) can be obtained from the graphs.

The position of a particle moving along x axis depends on the time according to the equation $\mathit{x}\mathbf{=}\mathit{c}{\mathit{t}}^{\mathbf{2}}\mathbf{‐}\mathit{b}{\mathit{t}}^{\mathbf{3}}$, where x is in meters and t in seconds. What are the units of –(a)Constant c and (b)Constant b? Let their numerical values be 2.0 and 3.0 respectively. (c) At what time does the particle reach its maximum positive x position? From $\mathit{t}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$ to $\mathit{t}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$. (d) what distance does the particle move? (e) what is its displacement? Find its velocity at times- (f) $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$ (g) $\mathit{t}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$(h) $\mathit{t}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$(i) $\mathit{t}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$ Find its acceleration at times- (j) $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$(k) $\mathit{t}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$(l) $\mathit{t}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$(m) $\mathit{t}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{s}$ .

An electron with an initial velocity${\mathbf{\text{V}}}_{\mathbf{0}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}$enters a region of length L=1.00cm where it is electrically accelerated. It emerges with$\mathbf{v}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{70}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{m}\mathbf{/}\mathbf{s}$. What is its acceleration, assumed constant?

Catapulting mushrooms. Certain mushrooms launch their spores by a catapult mechanism. As water condenses from the air onto a spore that is attached to the mushroom, a drop grows on one side of the spore and a film grows on the other side. The spore is bent over by the drop’s weight, but when the film reaches the drop, the drop’s water suddenly spreads into the film and the spore springs upward so rapidly that it is slung off into the air. Typically, the spore reaches the speed of 51.6 m/s in a $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{ }\mathit{\mu }\mathit{m}$ launch; its speed is then reduced to zero in 1.0 mm by the air. Using that data and assuming constant accelerations, (a) find the accelerations in terms of g during the launch. (b)Find the accelerations in terms of g during the speed reduction.

An electric vehicle starts from rest and accelerates at a rate of  $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$in a straight line until it reaches a speed of 20 m/s . The vehicle then slows at a constant rate of $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?

A muon (an elementary particle) enters a region with a speed of $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}$ and then is slowed down at the rate of $\mathbf{1}\mathbf{.}\mathbf{25}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. (a) How far does the muon take to stop? (b) Graph x vs t and v vs t for the muon.

An electron has a constant acceleration of +${}^{\mathbf{+}\mathbf{3}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}}$. At a certain instant, its velocity is +${}^{\mathbf{9}\mathbf{.}\mathbf{6}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}}$.What is its velocity (a) ${}^{\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{s}}$earlier and (b)${}^{\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{s}}$later?

On a dry road, a car with good tires may be able to brake with a constant deceleration of $\mathbf{4}\mathbf{.}\mathbf{29}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ . (a)How long does such a car, initially travelling at 24.6 m/s, take to stop? (b)How far does it travel in this time? (c)Graph x vs t and v vs t for the deceleration.

A certain elevator cab has a horizontal run of 190 m and a maximum speed of  305 m/min , and it accelerates from rest and then back to rest at $\mathbf{1}\mathbf{.}\mathbf{22}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. (a) How far does the cab move while accelerating to full speed from rest?  (b)How long does it take to make the nonstop 190 m run, starting and ending at rest?

The brakes on your car can slow you at a rate of $\mathbf{5}\mathbf{.}\mathbf{2}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. (a)If you are going  137 km/ h and suddenly see a state trooper, what is the minimum time in which you can get your car under the  90 km/ hspeed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun). (b)Graph x vs t and v vs t for such a slowing.

Suppose a rocket ship in deep space moves with constant acceleration equal to $\mathbf{9}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$, which gives the illusion of normal gravity during the flight. (a)If it starts from rest, how long will it take to acquire a speed one tenth of light (c=$\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}$ )? (b)How far will it travel in so doing.

A world’s land speed record was set by Colonel John P. Stapp when in March 1954, he rode a rocket propelled sled that moved along a track at${}^{\mathbf{1020}\mathbf{ }\mathbf{km}\mathbf{/}\mathbf{h}}$. He and the sled were brought to a stop in${}^{\mathbf{1}\mathbf{.}\mathbf{4}\mathbf{ }\mathbf{sec}}$. In terms of g, what acceleration did he experience while stopping?

A block of mass M is pulled along a horizontal frictionless surfaceby a rope of mass m, as shown in Fig. 5-63. A horizontal force $\overrightarrow{\mathbf{F}}$  acts on one end of the rope

.(a) Show that the rope must sag, even if only by an imperceptibleamount. Then, assuming that the sag is negligible, find 

(b) the accelerationof rope and block,

 (c) the force on the block from the rope, and 

(d) the tension in the rope at its midpoint.

A car travelling  56.0 km/ h is 24.0 m from the barrier when the driver slams on the brakes. The car hits the barrier 2.00 s  later. (a)What is the magnitude of the car’s constant acceleration before impact? (b)How fast is the car traveling at impact?

In figure, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to x axis. At time t=0, the red car is at ${\mathit{x}}_{\mathbf{r}}\mathbf{=}\mathbf{0}$and green car is at ${\mathbf{x}}_{\mathbf{g}}\mathbf{=}\mathbf{220}\mathbf{ }\mathbf{m}$. If the red car has constant velocity of 20 km/hr, the cars pass each other at x = 44.5 m, and if it has a constant velocity of  40 km/hr, they pass each other at  x = 76.6 m. What are (a) the initial velocity? (b) the constant acceleration of the green car?

Figure shows a red car and a green car that move toward each other. The other figure is a graph of their motion, showing their positions ${\mathbf{x}}_{\mathbf{g}\mathbf{0}}\mathbf{=}\mathbf{270}\mathbf{m}$ and  ${\mathbf{x}}_{\mathbf{r}\mathbf{0}}\mathbf{35}\mathbf{m}\mathbf{=}\mathbf{-}\mathbf{ }$ at time  $\mathbf{t}\mathbf{=}\mathbf{0}$.The green car has a constant speed of 20.0 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?

Figure depicts the motion of a particle moving along an x axis with a constant acceleration. The figure’s vertical scaling is set by ${\mathit{x}}_{\mathbf{s}}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{m}$. What are the (a) magnitude and(b) direction of particle’s acceleration?

(a) If the maximum acceleration that is tolerable for passengers in a subway train is$1.34m^2$   and subway stations are located  $\mathbf{806}\mathbf{ }\mathit{m}$ apart, what is maximum speed a subway train can attain between stations? (b)What is the travel time between stations? (c) If a subway train stops for $20 s$  at each station, what is the maximum average speed of the train, from one start up to the next? (d) Graph x, v and a versus t for the interval from one start-up to the next?

You are arguing over a cell phone while trailing an unmarked police car by $\mathbf{25}\mathbf{\hspace{0.33em}}\mathbf{m}$; both your car and the police car are traveling at $\mathbf{110}\mathbf{ }\mathbf{km}\mathbf{/}\mathbf{h}\mathbf{.}$ .Your argument diverts your attention from the police car for $\mathbf{ }\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{s}$, (long enough for you to look at the phone and yell, “I won’t do that!”). At the beginning of that $\mathbf{ }\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{s}$,the police officer begins braking suddenly at $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$(a)What is the separation between the two cars when your attention finally returns? Suppose that you take another $\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{ }\mathbf{s}$ to realize your danger and begin braking. (b)If you too brake at $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ ,what is your speed when you hit the police car?