The deceleration exerienced by a moving motor blat, after its engine is cut-off is given by `dv//dt=-kv^(3)`, where `k` is constant. If `v_(0)` is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time `t` after the cut-off is.

Explanation

`int (dv)/(v^3)= - int k" "dt, -1"/.2v^(2)= -kt+c`
But, `v= v_(0)," at "t=0`
Then `c= 1"/"2v_(0)^(2), 1"/"v^(2)= 1"/"v_(0)^(2)+2kt`
`v= v_(0)"/"sqrt(2v_(0)^(2)kt +1)`.