A body of 2kg has an initial speed `5ms^(-1)` . A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The force time graph is shown in figure. The final speed of the body is

Options

A. `9.25ms^_(-1)`
B. `5ms^_(-1)`
C. `14.25ms^_(-1)`
D. `4.25ms^_(-1)`

Answer

C

Explanation

Impulse=Change in momentum `=m(v_(2)-v_(1))` …(i)
Again impulse=Area between the graph and time axis
`=(1)/(2)xx2xx4+2xx4+(1)/(2)(4+2.5)xx0.5+2xx2.5`
`=4+8+1.625+5=18.625`
From (i) and (ii), `m(v_(2)-v_(1))=18.625`
`implies v_(2)=(18.625)/(m)=v_(1)=(18.625)/(2)+5=14.25m//s` .