A cheetah is hunting. Its prey runs for 4.3 s at a constant velocity of +8.4 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?

Well, let's do some math to find out! First of all, the distance the prey runs can be calculated using the formula: distance = velocity × time. So, the distance the prey runs is (8.4 m/s) × (4.3 s) = 36.12 meters.

Since the cheetah starts from rest, its initial velocity is 0 m/s. The distance the cheetah runs can be calculated using the formula: distance = initial velocity × time + 0.5 × acceleration × time^2.

We want the distance the cheetah runs to be the same as the prey, so we can set the distances equal to each other: 36.12 meters = 0 m/s × (4.3 s) + 0.5 × acceleration × (4.3 s)^2.

Now, let's solve for acceleration. By rearranging the equation: acceleration = (36.12 meters) / (0.5 × (4.3 s)^2) ≈ 0.97 m/s^2.

So, the cheetah needs to maintain a constant acceleration of approximately 0.97 m/s^2. But hey, if the cheetah wants to catch its prey, it better not be running like a clown!

To find the constant acceleration the cheetah must maintain in order to run the same distance as its prey in the same time, we can use the equation of motion:

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

For the prey:
distance_prey = velocity_prey * time

For the cheetah:
distance_cheetah = initial velocity_cheetah * time + (1/2) * acceleration_cheetah * time^2

Since both distances are the same, we have:

velocity_prey * time = initial velocity_cheetah * time + (1/2) * acceleration_cheetah * time^2

Simplifying the equation:

velocity_prey = initial velocity_cheetah + (1/2) * acceleration_cheetah * time

We know the values for velocity_prey (+8.4 m/s), time (4.3 s), and initial velocity_cheetah (0 m/s). Let's solve for acceleration_cheetah:

8.4 m/s = 0 m/s + (1/2) * acceleration_cheetah * 4.3 s

Multiply both sides by 2 to isolate acceleration_cheetah:

16.8 m/s = acceleration_cheetah * 4.3 s

Divide both sides by 4.3 s to solve for acceleration_cheetah:

acceleration_cheetah = 16.8 m/s / 4.3 s

acceleration_cheetah ≈ 3.907 m/s^2

Therefore, the cheetah must maintain a constant acceleration of approximately 3.907 m/s^2 in order to run the same distance as its prey runs in the same time.

To determine the constant acceleration the cheetah must maintain, we first need to calculate the distance the prey runs. This can be done using the equation:

distance = velocity * time

Given that the prey runs at a constant velocity of +8.4 m/s for 4.3 s, we can calculate the distance:

distance = 8.4 m/s * 4.3 s
distance = 36.12 m

Now, since the cheetah needs to run the same distance in the same time, we can use the equation of motion:

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

The initial velocity of the cheetah is 0 m/s as it starts from rest. The time is also 4.3 s, and the distance is 36.12 m. We can rearrange the equation to solve for acceleration:

distance - initial velocity * time = (1/2) * acceleration * time^2

36.12 m - 0 m/s * 4.3 s = (1/2) * acceleration * (4.3 s)^2

36.12 m = (1/2) * acceleration * 18.49 s^2

Solving for acceleration:

acceleration = (36.12 m / (1/2 * 18.49 s^2)

acceleration = 3.90 m/s^2

Therefore, the cheetah must maintain a constant acceleration of 3.90 m/s^2 in order to run the same distance as its prey in the same time.

d = 8.4m/s * 4.3s = 36.12m = Distance prey runs.

d = 0.5at^2 = 36.12m,
d = 0.5 * a(4.3)^2 = 36.12m,
d = 9.245a = 36.12,
a = 36.12 / 9.245 = 3.91m/s^2.