Question

What is the kinetic energy of an object with a mass of `16 kg` that has been in freefall for `2 s`?

Answer 1

`3000J`

Explanation:

Recall that the formula for kinetic energy is:

`color(blue)(|bar(ul(color(white)(a/a)DeltaE_k=1/2mDeltav^2color(white)(a/a)|)))`

where:
`DeltaE_k=`change in kinetic energy
`m=`mass
`Deltav=`change in velocity

Step 1
In order to use the kinetic energy formula, you first need to determine the initial velocity, which can be found by using the rearranging the formula for acceleration.

`a=(Deltav)/(Deltat)`

`a=(v_f-v_i)/(Deltat)`

`aDeltat=v_f-v_i`

`v_i=v_f-aDeltat`

Step 2
Substitute `v_i=v_f-aDeltat` into the kinetic energy formula.

`DeltaE_k=1/2mDeltav^2`

`DeltaE_k=1/2m(v_f-v_i)^2`

`DeltaE_k=1/2m(v_f-color(darkorange)((v_f-aDeltat)))^2`

`DeltaE_k=1/2m(aDeltat)^2`

Plug in the values.

`DeltaE_k=1/2(16kg)((9.81m/s^2)(2s))^2`

Solve.

`DeltaE_k=1/2(16kg)(384.9444m^2/s^2)`

`DeltaE_k=3079.5552J`

`DeltaE_k=color(green)(|bar(ul(color(white)(a/a)color(black)(3000J)color(white)(a/a)|)))`