Under the influence of a force, an object of mass 4 kg accelerates from 3 m/s to 6 m/s in 8s. How much work was done on the object during this time?

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Answer 1 · 2016-12-31T10:51:16

54 J

We can use Newton's 2nd Law to find the magnitude of the force:

#sf(F=ma)#

The acceleration a is the rate of change of velocity:

#sf(a=(DeltaV)/t=(6-3)/8=0.375color(white)(x)"m/s"^2)#

#:.##sf(F=4xx0.375=1.5color(white)(x)N)#

The work done is the force x the distance travelled in the direction of the force.

To find the distance travelled during this time we can use:

#sf(v^2=u^2+2as)#

#:.##sf(6^2=3^2+(2xx0.375xxs)#

#sf(36=9+0.75xxs)#

#sf(s=27/0.75=36color(white)(x)m)#

#sf(W=Fxxs=1.5xx36=54color(white)(x)J)#