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AP Physics C: Mechanics
4.2 Change in Momentum and Impulse
BeginnerMCQMathematical15.6k
A graph of force F versus time t. The horizontal axis is labeled time t, with tick marks at 0, T/2, and T. The vertical axis is labeled force F, with a tick mark at F_0. A smooth, symmetric curve starting at the origin (0, 0), rising to a peak of F_0 at t = T/2, and returning to 0 at t = T, representing one half-cycle of a sine wave labeled F(t) = F_0 sin(pi t / T). No other labels, lines, text, or axes appear.
Force as a function of time.
A block of mass \(m\) is initially at rest on a frictionless horizontal surface. Starting at time \(t = 0\), a time-varying force \(F(t) = F_0 \sin\left(\dfrac{\pi t}{T}\right)\) is exerted on the block in the positive x-direction for the time interval \(0 \le t \le T\), where \(F_0\) and \(T\) are positive constants. What is the change in velocity of the block during this time interval?

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