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

Step-by-step solution

P = 3 t 2 - 2 t + 1 = d E d t ∴ d E = ( 3 t 2 - 2 t + 1 ) d t E = ∫ t = 2 s t = 4 s ( 3 t 2 - 2 t + 1 ) d t = 3 t 3 3 - 2 t 2 2 + t t = 2 s t = 4 s = [ 4 3 - 2 3 - 4 2 - 2 2 + ( 4 - 2 ) ] E = 56 - 12 + 2 = 46 J