3 The cheetah is the fastest land mammal, reaching a top speed of 75 mph. One of

Question

3 The cheetah is the fastest land mammal, reaching a top speed of 75 mph. One of its major food sources, the impala, has a top speed of 50 mph, but it often able to escape by running in zigzags. a The cheetah can accelerate from 0 to 60 mph in three seconds. If it maintains this acceleration, how long does it take for the cheetah to further accelerate to full speed? b The cheetah spots an impala. The impala takes off with a constant ac- celeration. It emerges from behind a rock, continues to accelerate, and runs past a tree 6.5 seconds later. The tree and the rock are 91 m apart. When the impala passes the tree, it's running hard at 20 m/s. Find the impala's speed when it passed the rock. c Find the acceleration of the impala.

Explanation / Answer

here,

a)

initial speed for cheetah , u1 = 0 mph

final speed , v1 = 60 mph = 26.8 m/s

time taken , t = 3 s

let the acceration be a1

v1 = 0 + a1 * t

26.8 = 0 + a1 * 3

a1 = 8.93 m/s^2

b)

final speed of impala ,v2 = 20 m/s

time taken , t2 = 6.5 s

s = 91 m

let the initial speed be u2

let the accelration be a2

s = u2 * t2 + 0.5 * a2 * t2^2

91 = u2 * 6.5 + 0.5 * a2 * 6.5^2 ....(1)

and

v2^2 - u2^2 = 2 * a2 * s

20^2 - u2^2 = 2 * a2 * 91 ....(2)

from (1) and (2)

u2 = 8 m/s

a2 = 1.85 m/s^2

the speed of impala when it passes the tree is 8 m/s

c)

the accelration of impala is 1.85 m/s^2

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