Please show work and Explain!! The cheetah is considered the fastest running ani

Question

Please show work and Explain!!

The cheetah is considered the fastest running animal in the world. Cheetahs can accelerate to a speed of 20.1 m/s in 2.50 s and can continue to accelerate to reach a top speed of 28.1 m/s. Assume the acceleration is constant until the top speed is reached and is zero thereafter.

1) Starting from a crouched position, how long does it take a cheetah to reach its top speed? (Express your answer to three significant figures.) s

2) How far does it travel in that time? (Express your answer to three significant figures.) m

3) If a cheetah sees a rabbit 120 m away, how long will it take to reach the rabbit, assuming the rabbit does not move? (Express your answer to three significant figures.) s

Explanation / Answer

here,

for v1 = 20.1 m/s and t1 = 2.5 s

let the accelration of cheetah be a

v1 = 0 + a * t1

20.1 = 0 + a * 2.5

a = 8.04 m/s^2

1)

let the time taken by cheetah to reach top speed , v = 28.1 m/s be t

v= 0 + a * t

28.1 = 0 + 8.04 * t

t = 3.5 s

the time taken is 3.5 s

2)

the distance travelled in this time , d = 0 * t + 0.5 * a * t^2

d = 0 + 0.5 * 8.04 * 3.5^2

d = 49.1 m

3)

distance of rabbit , d1 = 120 m

the cheetah will travell first 49.1 m in 3.5 s and thereafter (120 -49.1) m at constant speed of 28.1 m/s

so the total time taken , t' = 3.5 + (120 - 49.1)/28.1

t' = 6.02 s

the total time taken to reach rabbit is 6.02 s

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