Cheetahs can accelerate to a speed of 21.9 m/s in 2.40 s and can continue to acc

Question

Cheetahs can accelerate to a speed of 21.9 m/s in 2.40 s and can continue to accelerate to reach a top speed of 29.7 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.

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

2) Starting from a crouched position, how much time taccel does it take a cheetah to reach its top speed

3) What distance d does it travel in that time?

4) If a cheetah sees a rabbit 126.0 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?

Explanation / Answer

1)

1 m/s = 2.23694 mile/hr

top speed = 29.7 m/s = 66.43701 miles/hr

here,

for v1 = 21.9 m/s and t1 = 2.40 s

let the accelration of cheetah be a

v1 = 0 + a * t1

21.9 = 0 + a * 2.4

a = 9.125 m/s^2

2)

let the time taken by cheetah to reach top speed , v = 29.7 m/s be t

v= 0 + a * t

29.7 = 0 + 9.125 * t

t = 3.255 s

the time taken is 3.255 s

3)

the distance travelled in this time ,

d = 0*t + 0.5*a*t^2

d = 0 + 0.5 * 9.125 * 3.255^2

d = 48.33 m

4)

distance of rabbit , d1 = 126 m

cheetah will travell first 48.33 m in 3.255 s and thereafter (126 - 48.33) m at constant speed of 29.7 m/s

so the total time taken , t' = 3.255 + (126 - 48.33) / 29.7

t' = 2.725 s

the total time taken to reach rabbit is 2.725 s

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.