Question

1. Cheetahs can accelerate to a speed of 20.0 m/s in 2.50 s and can continue to accelerate to reach a top speed of 27.6 m/s. Assume the acceleration is constant until the top speed is reached and is zero thereafter. Let the +?+x direction point in the direction the cheetah runs.

Express the cheetah's top speed ?top in miles per hour (mi/h)(mi/h) .

vtop =

Starting from a crouched position, how much time ?accel does it take a cheetah to reach its top speed and what distance ?d does it travel in that time?

taccel =

d=

If a cheetah sees a rabbit 132.0 m away, how much time ttotal will it take to reach the rabbit, assuming the rabbit does not move and the cheetah starts from rest?

ttotal=

2.

Very large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (??SI), defined as ??=?5/2?SI=a5/2t . In the expression, ?t is the duration of the accleration, but ?a is not equal to the acceleration. Rather, ?a is a dimensionless constant that equals the number of multiples of ?g that the acceleration is equal to.

In one set of studies of rear-end collisions, a person's velocity increases by 17.3 km/h with an acceleration of 34.0 m/s2 . Let the +?+x direction point in the direction the car is traveling. What is the severity index for the collision?

??=

How far ? does the person travel during the collision if the car was initially moving forward at 5.70 km/h ?

?=

Answer 1

2o a(9.so) 2) 132 m tolal tt. 3.us+C13241.с) linnu tete n 23.L 3 Co a as

ash t 2 S 1.533/sc -1.683 (O、(W3) +2 (34) (0-1413)"