A particle of mass m moving along the x-axis experiences the net force Fx=ct, where c is a constant. The particle has velocity v0x at t = 0. Find an algebraic expression for the particle's velocity vx at a later time t. Express your answer in terms of the variables c, t, v0x, and m.

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”