Question

Power applied to a particle varies with time as $P=(3t^2-2t+1)$ watt, where t is in second. Find the change in its kinetic energy between time t=2s and t=4s.

• A. 32 J
• B. 46 J
• C. 61 J
• D. 102 J

Answer 1

The correct option is B

46 J

Change in kinetic energy ($\Delta$k) is nothing but work-done (w)
We have, $P=3t^2-2t+1$
$\frac{dw}{dt}=3t^2-2t+1$
$\int dw=3\underset{2}{\overset{4}{\int }}{t}^{2}dt-2\underset{2}{\overset{4}{\int }}dt+\underset{2}{\overset{4}{\int }}dt$
$w=3\frac{t^3}{3}{|}_2^4-2\frac{t^2}{2}{|}_2^4+t{|}_2^4$
w=(64-8)-(16-4)+(4-2)
w=46 J