The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of tL=0.5s. The force as a function of time is given by F(t)=at2+b, where a=−28N/s2 and b=7.0N . The momentum of the t-shirt will be its initial momentum (p0=0) plus its change in momentum due to the applied impulse: pf=p0+∫t=tLt=0F(t)dt. By applying the given time dependent function for F(t) and performing the integration, which of the following is the correct expression for pf?

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