Vinny is on a motorcycle at rest, 200 m away from a ramp that jumps over a gully. Calculate the minimum constant acceleration Vinny must have to get to the ramp in 8 s before his pursuers catch up with him.

6.25 m/s^2

Explanation:

The distance between Vinny and the ramp is 200m

And he has 8 seconds (At max) to reach that distance.

The initial velocity is 0m/s

The initial position is 0m

Now, we want to find the constant acceleration in order to do this, so suppose that we have a constant acceleration A.

a(t) = A.

To have the velocity, we must integrate over time, and remember that the constant of integration is equal to zero because the initial velocity is zero.

v(t) = A*t

For the position, we integrate again over time.

p(t) = 0.5*A*t^2

And we want to travel 200m in 8 seconds, then:

p(8s) = 200m

0.5*A*(8s)^2 = 200m

A*32s^2 = 200m

A = 200m/32s^2 = 6.25 m/s^2

This is the minimum acceleration in order to do this, if Vinny has a larger acceleration he will travel the 200m in a smaller time.

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

answer: a. same unit

explanation: