Question

The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45m in a straight line, reaching a final speed of 72 km/h.

Determine the cheetah's average acceleration during the short sprint and find its displacement at t= 3.5s

Answer 1

The cheetah's average acceleration during the short sprint is 5.71 m/s², and its displacement at t = 3.5 s is 25 m.

Step-by-step explanation:

The cheetah's average acceleration can be determined using the equation:

acceleration = (final velocity - initial velocity) / time

Given that the cheetah starts from rest and reaches a final speed of 72 km/h (20 m/s) in a time of 3.5 seconds, we can plug in the values to find:

acceleration = (20 m/s - 0 m/s) / 3.5 s = 5.71 m/s²

To find the cheetah's displacement at t = 3.5 s, we can use the equation:

displacement = initial velocity * time + (1/2) * acceleration * time^2

Since the cheetah starts from rest, the initial velocity is 0 m/s. Plugging in the values:

displacement = 0 m/s * 3.5 s + (1/2) * 5.71 m/s² * (3.5 s)^2 = 25 m