Question #e2a90

1 Answer
Feb 3, 2017

Answer:

#8(1+t)" Js"^-1#

Explanation:

We know that Kinetic Energy of an object having mass #m# and velocity #v# is given by the expression

#KE=1/2mv^2# .....(1)

Also kinematic equation connecting quantities of interest is

#v=u+at#.....(2)
where #u# is initial velocity, #a and t# are acceleration and time respectively.
Inserting value of #v# from (2) in (1) we get
#KE=1/2m(u+at)^2#

To find rate of change of kinetic energy we differentiate both sides with respect to time. We get

#dot(KE)=d/dt[1/2m(u+at)^2]#

using chain rule we get
#dot(KE)=1/2m[2(u+at)xxa]#

Inserting given values we get
#dot(KE)=1/2xx2[2(2+2t)xx2]#
#dot(KE)=8(1+t)" Js"^-1#