Help - Uniform Acceleration Problem

[petuniac]

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?

Answer is : 3.0 m/s^2

How do you do this problem??

Thanks!

 

[civil_dude]

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.

 

[petuniac]

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

 

[petuniac]

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]

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'.

 

[petuniac]

Thanks! Got it now :)