Two cars are driving at the same constant speed on a

straight road, with car 1 in front of car 2. Car 1 suddenly starts

to brake with constant acceleration and stops in 10 m. At the

instant car 1 comes to a stop, car 2 begins to brake with the

same acceleration. It comes to a halt just as it reaches the back of car 1. What was the separation between the cars before they starting braking?

A small child gives a plastic frog a big push at the bottom of a slippery 2.0-m-long, 1.0-m-high ramp, starting it with a speed of 5.0 m/s. What is the frog’s speed as it flies off the top of the ramp?

FIGURE EX2.7 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat?

FIGURE EX2.7 showed the velocity graph of blood in the aorta. What is the blood’s acceleration during each phase of the motion, speeding up and slowing down?

Careful measurements have been made of Olympic sprinters in the 100 meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.6 m/s² for $3\frac{1}{3}s$, then runs at constant velocity to the finish line.

a. What is the race time for a sprinter who follows this model?

b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter’s top speed is the same as in part a, what acceleration would he need to run the 100 meter dash in 9.9 s?

c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by 1%?

A particle moving along the x-axis has its velocity described by the function $v_x=2t^2$ m/s, where t is in s. Its initial position is x0 = 1 m at t0 = 0 s. At t = 1 s what are the particle’s (a) position, (b) velocity, and (c) acceleration?