Kevin S. Huang

2014: Problem 9

Topic: Collisions
Concepts: Impulse-momentum theorem

Solution:

Recall the area under a $F$ – $t$ plot corresponds to the impulse $J$ . By the impulse-momentum theorem,

J=\Delta p=p_f-p_i=m(v_f-v_i)

Solving for the final velocity $v_f$ ,

v_f=v_i+\frac{J}{m}

In our case, going from $t=0\,\mathrm{s}$ to $7\,\mathrm{s}$ , we have $J=12.5\,\mathrm{kg\,m/s}$ so

v_f=1\,\mathrm{m/s}+\frac{12.5\,\mathrm{kg\,m/s}}{5\,\mathrm{kg}}=3.5\,\mathrm{m/s}

Thus, the answer is C.