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

Answer:

#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)|)))#