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

1 Answer
May 15, 2016

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)|)))