Question

Finally, you are ready to answer the main question. Cheetahs, the fastest of the great cats, can reach 50.0 miles/hour miles/hour in 2.22 s s starting from rest. Assuming that they have constant acceleration throughout that time, find their acceleration in meters per second squared.

Answer 1

Answer:

a = 10.07m/s^2

Their acceleration in meters per second squared is 10.07m/s^2

Explanation:

Acceleration is the change in velocity per unit time

a = ∆v/t

Given;

∆v = 50.0miles/hour - 0

∆v = 50.0miles/hours × 1609.344 metres/mile × 1/3600 seconds/hour

∆v = 22.352m/s

t = 2.22 s

So,

Acceleration a = ∆v/t = 22.352m/s ÷ 2.22s

a = 10.07m/s^2

Their acceleration in meters per second squared is 10.07m/s^2

Answer 2

Answer:

10.1m/s²

Explanation:

Using one of the equations of motion as follows;

v = u + at       ----------------------(i)

where;

v = final velocity of the body (Cheetahs) = 50.0 miles/hour

u = initial velocity of the body = 0 (since they start running from rest)

a = acceleration/deceleration

t = time taken for the motion = 2.22s

First convert the final velocity (v) from miles/hour to m/s

Remember that;

1 mile = 1609.34m

1 hour = 60 x 60s = 3600s

Therefore;

50miles/hour = $\frac{50miles}{1 hour}$ = $\frac{50*1609.34m}{3600s}$ = 22.35m/s

=> v = 22.35m/s

Substituting the values of v, u and t into equation (i) gives;

=> 22.35 = 0 + a (2.22)

=> 22.35 = 2.22a

=> a = $\frac{22.35}{2.22}$ = 10.07m/$s^{2}$

=> a = 10.1m/s² (to 1 decimal place)

Therefore the acceleration in m/s² is 10.1