Question #90693

1 Answer
Jan 31, 2017

Recall the Newton' second Law of motion for an object of mass #m# acted upon a force #vecF#
#vecF=mveca# ......(1)
where #veca# is the acceleration produced.

If a force acts through a displacement #vecs#,
Work done #W=vecFcdot vecs# .....(2)
Using (1) we can write (2) as
#W=mvecacdot vecs# ....(3)

Recall the kinematic equation
#vecv^2-vecu^2=2vecacdot vecs# .....(4)
where #vecu# is the initial velocity, #vecv# is the final velocity.

Using (4) equation (3) becomes*
#W=1/2m(vecv^2-vecu^2)#
Inserting given values
#W=1/2xx8.1((9.6hati+2.3hatj)^2-(9.9hati+6.0hatj)^2)#
We know that square of a vector is dot product of vector with itself hence, above equation becomes
#W=1/2xx8.1((9.6^2+2.3^2)-(9.9^2+6.0^2))#
#=>W=-148.1J#

*recall that equation is #W=("Final kinetic energy"-"Initial Kinetic energy")#