An object of mass 500 g , initially at rest , is acted upon by a variable force whose X - component varies with X in the manner shown . The velocites of the object at the points X = 8 m and X = 12 m , would have the respective values of (nearly )

Options

A. 18 m/s and 20.6 m/s
B. 18 m/s and 24.4 m/s
C. 23 m/s and 24.4 m/s
D. 23 m/s and 20.6 m/s

Answer

B

Explanation

From work energy theorem , we can say that work done is equal to change in kinetic energy .
From x = to x = 8 m , `1/2mv^(2) = 100 +30`
`v = sqrt(520) = 23` m/s
`1/2 mv^(2) = 100 +30 - 47.5 +20`
`v cong sqrt(410)`
`v = 20.6 ` m/s
Hence appropriate option in 23 m/s and 20.6 m/s