What is the acceleration of the cart down the incline?

[KAW008]

Question: Suppose you have measured the time (delta T) required for a glider to travel several distances (delta X) down an inclined plane. After plotting the data points on a graph of delta X vs. (delta T)^2, you find the slope of the best fitting straight line is 15cm/s^2. What is the acceleration of the cart down the incline?

I am have such difficulty trying to figure out where to start with this problem. I know that slope = rise/run and that Acceleration = the limit of delta V/ delta T, as T goes to zero. If someone could please point me in the right direction to figuring it out, it would be greatly appreciated!

 

[Curious3141]

Do you know the relationship between distance traveled and time under constant acceleration. Ther is a basic kinematics equation here :

$$s = ut + \frac{1}{2}at^2$$ where s is the distance travelled, u is the initial velocity, a is the (constant) acceleration and t is the time elapsed.

For your problem, you can let the initial velocity be zero (the glider starts at rest). Use the equation to figure out how the acceleration relates to the gradient of the straight line obtained by plotting $$s$$ vs $$t^2$$.

 

[Curious3141]

BTW, I'm fairly certain this doesn't belong in the College section.