Q10E - University Physics with Modern Physics

Question

A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.10 At which of the labeled points is her velocity (a) zero? (b) constant and positive? (c) constant and negative? (d) increasing in magnitude? (e) decreasing in magnitude?

Step-by-Step Solution

Answer

a.The velocity is zero atpoint (IV) 

b.The velocity isconstant and positive at point (I) 

c.The velocity is constant and negative at point (V) 

d.The velocity is Increasing in magnitude at Point (II) 

e.The velocity is decreasing in magnitude at point (III)

Step 1: Definition of the velocity

Velocity refers to the ratio of change in displacement with respect to time.

$v=\frac{dx}{dt}$

Where,  are the displacement and time, respectively.

 The velocity can be visualized as the slope of the x-t curve

Step 2: Explanation of the zero velocity

Atpoint (IV) the value of the slope is zero because displacement is constant with time,therefore, thevelocity is zero.

Step 3: Explanation of constant and positive velocity

At point (I) the displacement is increasing with time at a constant positive rate, which implies that the slope is constant and has a positive value. Therefore, the velocity is constant and positive.

Step 4: Explanation of constant and negative velocity

At point (V) the displacement starts decreasing with time at a constant negative rate, which implies that the velocity has a negative and constant value.

Step 5: Explanation of increasing velocity

At point (II) the slope is increasing with the positive value. Therefore, velocity will increase.

Step 6: Explanation of decreasing velocity

At point (III) the value of slope starts reducing as compared to the point (II), therefore it means that the velocity is decreasing, as the direction is opposite to that of the increasing velocity.