An object with a mass of #2 kg# is moving at #7 m/s# over a surface with a kinetic friction coefficient of #1 #. How much power will it take to accelerate the object at #4 m/s^2?

1 Answer
Jan 8, 2017

The power that much be supplied at the moment #v=7m/s# is #193.2 W#

Explanation:

The power expended on an object can be found by multiplying the force applied to the object by the speed of the object's motion.

#P=Fxxv#

To cause acceleration of #4m/s^2# we require a net force of

#F_"net"=ma = (2kg)(4m/s^2)=8 N#

Since there is a frictional force present, this net force is composed of two separate forces

#vecF_"net"= vecF_"applied"+vecF_f#

where the force of friction will equal #mumg#, and #mu = 1#

So,

#8N = F_"applied" - (2)(9.8)#

"F_"applied"= 8 + 19.6 = 27.6N#

At the moment the acceleration begins, #v=7m/s#, and the power expended is

#P=F_"appied" xx v=(27.6N)(7m/s)= 193.2W#

Note that as the speed increases, the power required to maintain this acceleration will increase, so the above answer is true only at the moment v = 7 m/s.