A force `F_1` acts on a particle so as to accelerate it from rest to a velocity v. The force `F_1` is then replaced by `F_2` which decelerates it to rest

Options

A. `F_(1)`is always equal to `F_(2)`
B. `F_(2)`is greater than `F_(1)`
C. `F_(2)` may be smaller than, greater than or equal to `F_(1)`
D. `F_(2)` cannot be equal to `F_(1)`

Answer

C

Explanation

During acceleration
`v = a_(1) t_(1) = (F_(1))/(m) t_(1)`
`F_(1) = (m v)/(t_(2)` …(i)
During retardation,
`0 = v - a_(2) t_(2) = v - (F_(2))/(m)`
`:. F_(2) = (m v)/(t_(2)` …(ii)
If `t_(1) = t_(2)` then `F_(1) = (F_(2))`
`t_(1) lt t_(2)` then `F_(1) gt (F_(2))` and
`t_(1) gt t_(2)` then `F_(1) lt (F_(2))`