Question

A cheetah is hunting. Its prey runs for 3.80 s at a constant velocity of +9.80 m/s. Starting from rest, what constant acceleration must the cheetah maintain in order to run the same distance as its prey runs in the same time?

Answer 1

The cheetah must maintain a constant acceleration of 5.16 m/s^2 to cover the same distance as its prey, which moves at 9.80 m/s for 3.80 seconds.

Step-by-step explanation:

The student has asked what constant acceleration a cheetah must maintain to run the same distance as its prey, which is running at a constant velocity of +9.80 m/s for 3.80 seconds. To find the cheetah's required acceleration, we use the kinematic equation for uniformly accelerated motion, which is x = x_0 + v_0t + ½ at^2, where x is the final position, x_0 is the initial position, v_0 is the initial velocity, a is the acceleration, and t is the time.

Since the cheetah starts from rest, v_0 is 0, and the initial position x_0 can be taken as 0 as well. Therefore, the equation simplifies to x = ½ at^2. The prey's constant velocity means its acceleration is 0, so its displacement x can be calculated using x = vt. Setting the prey's distance equal to the cheetah's distance gives us 9.80 m/s × 3.80 s = ½ a × (3.80 s)^2.

Solving for a:

a = × 2 × (9.80 m/s × 3.80 s) / (3.80 s)^2

a = 5.16 m/s^2

Therefore, the cheetah must maintain a constant acceleration of 5.16 m/s^2 to cover the same distance as its prey in the same amount of time.