Question

A time-varying net force acting on a 4.0-kg particle causes the particle to have a

displacement given by x = 2.0 t - 3.0 t2 + 1.0 t3

, where x is in meters and t is in seconds.

(a) Use Work- energy theorem to find the work done on the particle in the first 3.0 s of motion.

(b) The average power delivered in the first 3 s.

(c) the instantaneous power delivered at t = 2 s.

Answer 1

(a) $v(t)=2-6t+3t^2$ ; $t=0\to v_0=2\ (m/s)$

$t=3\ s\to v=11\ (m/s)$

$W=\Delta KE=mv^2/2-mv_0^2/2=(m/2)(v^2-v_0^2)=$

$=(4/2)(11^2-2^2)=234\ (J)$

(b) $P_{avr}=W/t=234/3=78\ (W)$

(c) $P(2)=F\cdot v=m(6t-6)(2-6t+3t^2)=$

$=4\cdot(6\cdot2-6)(2-6\cdot2+3\cdot2^2)=48\ (W)$