Answer: 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.
