A 15kg block is initially moving along a smooth horizontal surface with a speed of `v=4m//s` to the left. It is acted by a force `F` , which varies in the manner shown. Determine the velocity of the block at `t=15` seconds.

Options

A. `12.5m//s`
B. `8.5m//s`
C. `20m//s`
D. `9.5m//s`

Answer

A

Explanation

Change in linear momentum `DeltaP=intFdt`
`15(v_(f)+u)=int_(0)^(15)40cos((pi)/(10))tdt`
`v_(f)=-4+(40)/(15)[(sin(pi//10)t)/(pi//10)]_(0)^(15)`
`=-4=(400)/(15pi)(-1)=-12.5m//s` .