A particle of mass $5.7 \mathrm {~kg}$, initially at rest, experiences a time-varying force, $f ( t ) = c t ^ { 2 } + h t$, where $c = 1.3 \mathrm {~N} / \mathrm { s } ^ { 2 }$ and $h = 5.6 \mathrm {~N} / \mathrm { s }$. What is the displacement of the particle at time $t = 4$ seconds?
A) 20 m
B) 15 m
C) 10 m
D) 25 m

Question

Quizplus · Accepted Answer

The displacement of the particle can be found by integrating the acceleration, which is obtained by dividing the force by the mass, twice with respect to time. The force function is $f(t) = 1.3t^2 + 5.6t$. The acceleration $a(t)$ is $f(t)/m = (1.3t^2 + 5.6t)/5.7$. Integrating this acceleration function with respect to time gives the velocity function, and integrating again gives the displacement function. After performing these integrations and evaluating at $t = 4$ seconds, the displacement is found to be 15 meters.

A Particle of Mass 5.7 kg5.7 \mathrm {~kg}5.7 kg , Initially at Rest, Experiences a Time-Varying Force

A Particle of Mass $5.7 \mathrm {~kg}$ , Initially at Rest, Experiences a Time-Varying Force