Question

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 t1 = 0.5 s. The force as a function of time is given by F(t) = ať+ b, where a = –28 N/s2 and b = 7.0 N. The momentum of the t-shirt will be its initial momentum (po 0) plus its change in momentum due to the applied impulse: pf = po+SET+ F(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?
a) tl tl Pf= 0++)16
b) 0+*+*+b)
c) 0+++bt) 0++) ti

Answer 1

Answer:

Follows are the solution to this question:

Explanation:

By checking the value in which we have calculated by performing its differentiation of $\frac{a}{3}t^3+bt$, the correct form of its integer value is calculating  with regard to t, that also provides as expected $at^2+b = F(t)$.