# Help - Uniform Acceleration Problem

Question is:

A boy on a skateboard accelerates uniformly down a hill, starting from rest. During the third one second interval from rest, he travels 7.5 m. What is the rate of acceleration of the skateboarder?

How do you do this problem??

Thanks!

I do it graphically, find the area under the line between t=2 & t=3 and let it equal the distance. It is linear, so it is easily solved this way.

how do you graph when you don't have the slope of the line?

Hmm.. I think I'm missing something easy here. In order to calculate the area under the graph I need to know the velocity at time t=2 s and the velocity at time t = 3s. I'm not sure how to find this given only that v(initial) = 0 and d (between 2 and 3s) = 7.5 m....

Any help would be greatly appreciated.

Astronuc
Staff Emeritus
OK, rather than do it graphically, let's try an algebraic method.

Take x(t) = 1/2 a t2, the general expression for distance as a function of 'constant' acceleration, i.e. accelerates uniformly.

Now let x(t=2s) = L = 1/2 a (2)2 (Eq 1), but that leaves two unknowns L and the acceleration a.

However, since we know that between 2s and 3s, the object move 7.5 m, then

let x(t=3s) = L + 7.5 m = . . . . (Eq 2)

then one had two unknowns and two equations. One can apply substitution, L from Eq 1 into L in Eq 2, and solve for 'a'.

Thanks! Got it now :)