A cart of mass m can move without friction on an air track. Initially, it is at

Question

A cart of mass m can move without friction on an air track. Initially, it is at rest. Then, for a limited time Delta t, it is pushed down the track with a constant force F. Which of the following statements are true? When you stop pushing, the cart starts slowing down again The higher the mass of the cart, the harder you have to push to achieve the same final speed in the same amount of time. You exert a larger force on the cart than the cart exerts on you. Leaving all other quantities unchanged, what happens in the scenarios below? bullet If you use a cart with half the mass, you cover distance during pushing. bullet If you use half the force, you reach final speed. bullet If you push half as long, you cover distance during pushing. bullet If you use a cart with half the mass, you reach final speed.

Explanation / Answer

1) When you stop pushing, the cart starts slowing down again =====>

2) The higher the mass of the cart, the harder you have to push to achieve the same final speed in the same amount of time. ========> TRUE

3)

B) i) If you use a cart with half the mass, you cover double the distance during pushing.

Halving the cart mass doubles the acceleration
F = ma
F = (½m)(2a)
With twice the acceleration, you get twice the distance
d = ½at²
2d = ½(2a)t²

ii) If you use half the force, you reach half the final speed.

F = ma
½F = m½a
and half the acceleration results in half the velocity
v = at
½v = ½at

iii) If you push half as long, you cover one fourth the distance during pushing.
d = ½at²
¼d = ½a(½t)²
¼d = ½a¼t²

iv)  If you half the mass of the cart, you reach double the final speed.

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