A block of mass `10 kg` is placed on a rough horizontal surface and is acted upon by a variable force `F` horizontaly. The coefficient of friction between block and surface is `mu`. The force `F` staring from a value of zero is increaseed linearly to `100 N` in `4 s` and then abruptly decreased to `40 N` which is then continued for `3 sec`. and then force is removed.

Options

A. The maximum velocity reached by the block is `5 m//s`
B. The time of motion of block is `5.4` sec.
C. The maximum velcotiy reached by the block is at time `2` sec. after the start of motion of the block
D. frication on block will be `25 N` at time `1 s` after the force begins to act

Answer

A, B, C, D

Explanation

at `t = 2 sec`. ltbRgt `F = 50 N` so motion of block starts
at `t = 4 s`
`J = P_(f) - P_(i)`
`(1)/(2) (100 + 50) xx 2 - 50 xx 2 = 10 v - 0`
`v = 5 m//s` at `t = 4 s` (maximum velocity)
after that `-50 xx (t - 7) = 0 - 10 xx 2`
`t = 7.4 s`
Time of motion `= 7.4 - 2 = 5.4 delta`
at `t = 1 , F = 25` ltbRgt `so `f = 25` , at `sumF = 0`