Question

Question #e2a90

Answer 1

`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`