Question

If you have a small cart or such that is free to roll, what happens if you give it many rapid, little pushes? You should give it several quick pushes over the second or so it is in motion. (You can watch the Introductory Lab Video to get a good idea of what we are asking - tap-tap- tap-tap-tap!) Then catch it to bring it to a stop. Discuss: what should a graph of position vs time look like? Velocity vs. time? What kind of motion are you modeling here?

Answer 1

If we are giving several small pushes quickly, It means Force applied is constant.

Therefore, Acceleration of the cart will be constant.

We know if the acceleration is constant, the Velocity-time graph will be linear and the distance time graph willbe parabolic.

This type of motion is called Uniformlu accelerate motion.

We can show this mathematically,

{ acceleration is constant }

After integrating, we will get.,

(Straight line eqation)

we can write again,

integrating again ,

so parablic function .