Sketch instantaneous acceleration vs. time graphs for a cart moving (1) with a constant acceleration, (2) with increasing acceleration, and (3) with decreasing acceleration. Write down the equation that best represents each of these graphs. If there are constants in your equation, what kinematic quantities do they represent?  How would you determine these constants from your graph? Which graph do you think best represents a cart rolling down an incline?

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  1. Sketch instantaneous acceleration vs. time graphs for a cart moving (1) with a constant acceleration, (2) with increasing acceleration, and (3) with decreasing acceleration. Write down the equation that best represents each of these graphs. If there are constants in your equation, what kinematic quantities do they represent?  How would you determine these constants from your graph? Which graph do you think best represents a cart rolling down an incline? 
  2. Write down a relationship between the acceleration and the velocity of the cart.  Use this to sketch a rough graph of instantaneous velocity vs. time for each of the three accelerations you drew in question one. Write down an equation that best represents each of these graphs*.  If there are constants in your equation, what kinematic quantities do they represent?  How would you determine these constants from your graph? Which graph do you think best represents the velocity of a cart rolling down an incline?

*SOLVE BOTH*

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