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

Options

A. `9.25 ms^(-1)`
B. `5 ms^(-1)`
C. `14.31 ms^(-1)`
D. `4.25 ms^(-1)`

Answer

C

Explanation

Impulse (I) = area under F – t graph
` = (1)/(2) xx 2 xx4 + 2xx4 + (1)/(2) ( 0.5) (4+2.5) + 2 xx 2.5`
` = 4+8+1.625 + 5 = 18.625`
Now, Impulse (I) = Change in moment
18.625 = `m (v_(f) - v_(i))`
`rArr v_(f) = v_(i) + (18.625)/(2) = 5+(18.625)/(2)`
`v_(f) = v_(i) + (18.625)/(2) = 5 + (18.625)/(2)`
`v_(f) = 14.31 m//s`