# Average Velocity Question (isolation?)

So there is this question i've been having trouble with for the past hour. It involved a child going down a ramp on a sled at and angle theta with a total system of mass. accelerates down a hill of length L during a time interval delta t. (this is literally all the question gives you, other than a really simple diagram which only indicates where the 0 is located)

So far I've figured out that a = gsin0.

The question it's asking me is the magnitude of the child's velocity is. (choices) The correct choice is e which is sqrt(gLsin0/2) How do they end up with this?

Any help would be appreciated.

• Using a zero as a theta is confusing. If you don’t know MathJax yet and can’t write $\sin{\theta}$, I suggest just writing it out as “sin(theta)”. – G. Smith Jan 5 at 21:48
• Your title indicates that you actually want the average speed, but your explanation makes it sound like you want the speed at the bottom of the hill. – G. Smith Jan 5 at 21:58

First of all you know the acceleration due to gravity is g ($$9.81 \frac{m}{s^2}$$).

Next you know, ignoring friction on the slide and air resistance, all masses have the same vertical acceleration g in a gravitational field.

Then you know the acceleration of the child is as a function of g, $$a=gsin$$.

Next, you know from kinematics that the distance traveled, which is $$L$$, is given by

$$L=\frac{at^2}{2}$$

From that you can calculate the time it takes the child to go distance $$L$$. Then finally you can calculate the velocity from

$$v=at$$

The answer they gave you is probably just a combination of these steps.

Hope this helps.