Chapter 2

At a track meet, a runner runs the 100 -m dash in 11.5 s. What was the runner's average speed?

A jogger jogs around a circular track with a diameter of \(300 \mathrm{m}\) in 10 min. What was the jogger's average speed in \(\mathrm{m} / \mathrm{s}\) ? What is the magnitude of the jogger's average velocity?

A group of college students eager to get to Florida on a spring break drove the 750 -mi trip with only minimum stops. They computed their average speed for the trip to be \(55.0 \mathrm{mi} / \mathrm{h}\). How many hours did the trip take?

A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of \(7.86 \times 10^{7} \mathrm{km} .\) Radio waves travel at the speed of light \(\left(3.00 \times 10^{8} \mathrm{m} / \mathrm{s}\right) .\) How many seconds does it take the signal to reach the Earth?

A student drives the 100 -mi trip back to campus after spring break and travels with an average speed of \(52 \mathrm{mi} / \mathrm{h}\) for 1 hour and 30 minutes for the first part of the trip. (a) What distance was traveled during this time? (b) Traffic gets heavier, and the last part of the trip takes another half- hour. What was the average speed during this leg of the trip? (c) Find the average speed for the total trip.

An airplane flying directly eastward at a constant speed travels \(300 \mathrm{km}\) in \(2.0 \mathrm{h}\). (a) What is the average velocity of the plane? (b) What is its instantaneous velocity?

A race car traveling northward on a straight, level track at a constant speed travels \(0.750 \mathrm{km}\) in 20.0 s. The return trip over the same track is made in \(25.0 \mathrm{s}\). (a) What is the average velocity of the car in \(\mathrm{m} / \mathrm{s}\) for the first leg of the run? (b) What is the average velocity for the total trip?

A sprinter starting from rest on a straight, level track is able to achieve a speed of \(12 \mathrm{m} / \mathrm{s}\) in \(6.0 \mathrm{s}\). What is the sprinter's average acceleration?

Modern oil tankers weigh more than a half-million tons and have lengths of up to one-fourth mile. Such massive ships require a distance of \(5.0 \mathrm{km}\) (about \(3.0 \mathrm{mi}\) ) and a time of 20 min to come to a stop from a top speed of \(30 \mathrm{km} / \mathrm{h}\). (a) What is the magnitude of such a ship's average acceleration in \(\mathrm{m} / \mathrm{s}^{2}\) in coming to a stop? (b) What is the magnitude of the ship's average velocity in \(\mathrm{m} / \mathrm{s}\) ? Comment on the potential of a tanker running aground.

A motorboat starting from rest travels in a straight line on a lake. (a) If the boat achieves a speed of \(8.0 \mathrm{m} / \mathrm{s}\) in \(10 \mathrm{s}\), what is the boat's average acceleration? (b) If the boat continues with the same acceleration, what would be its speed after another \(5.0 \mathrm{s}\) ?

A car travels on a straight, level road. (a) Starting from rest, the car is going \(44 \mathrm{ft} / \mathrm{s}(30 \mathrm{mi} / \mathrm{h})\) at the end of \(5.0 \mathrm{s}\). What is the car's average acceleration in ft/s \(^{2} ?\) (b) In 4.0 more seconds, the car is going \(88 \mathrm{ft} / \mathrm{s}\) ( \(60 \mathrm{mi} / \mathrm{h}\) ). What is the car's average acceleration for this time period? (c) The car then slows to \(66 \mathrm{ft} / \mathrm{s}\) ( \(45 \mathrm{mi} / \mathrm{h}\) ) in 3.0 s. What is the average acceleration for this time period? (d) What is the overall average acceleration for the total time? (Note these convenient British unit conversions: \(60 \mathrm{mi} / \mathrm{h}=88 \mathrm{ft} / \mathrm{s}, 45 \mathrm{mi} / \mathrm{h}=66 \mathrm{ft} / \mathrm{s},\) and \(30 \mathrm{mi} / \mathrm{h}=44 \mathrm{ft} / \mathrm{s} . \mathrm{J}\)

shows the Hoover Dam Bridge over the Colorado River at a height of \(274 \mathrm{m}\) If a heavy object is dropped from the bridge, how much time passes before the object makes a splash?

A spaceship hovering over the surface of Mars drops an object from a height of 30 m. How much longer does it take to reach the surface than if dropped from the same height on Earth? Neglect air resistance in both cases. [The acceleration due to gravity on Mars is \(33 \%\) of that on Earth, \(\left.g_{\text {mars }}=(0.33) g .\right]\)

A race car goes around a circular, level track with a diameter of \(1.00 \mathrm{km}\) at a constant speed of 90.0 km/h. What is the car's centripetal acceleration in \(\mathrm{m} / \mathrm{s}^{2}\) ?

A person drives a car around a circular, level cloverleaf with a radius of \(70 \mathrm{m}\) at a uniform speed of \(10 \mathrm{m} / \mathrm{s}\). (a) What is the acceleration of the car? (b) Compare this answer with the acceleration due to gravity as a percentage. Would you be able to sense the car's acceleration if you were riding in it?

If you throw a baseball horizontally with an initial speed of \(30 \mathrm{m} / \mathrm{s}\) from a height of \(2.0 \mathrm{m}\), how long will it take the ball to hit the ground?

A golfer on a level fairway hits a ball at an angle of \(42^{\circ}\) to the horizontal that travels 100 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 100 yd. At what angle was the second ball hit? (Neglect air resistance.