A car `C` of mass `m` is initially at rest on the boat `A` of mass `M` tied to the identical boat `B` of some, mass `M` through a massless inextensible string as shown in the figure. The car accelerates from rest to velocity `v_(0)` with respect to boat `A` in time `t_(0)sec`. At time `t=t_(0)` the car applies brake and comes to rest relative to boat in negligible time. Neglect friction between boat and water find the velocity of boat `A` just after applying brake.

Explanation

`A` the car `C` accelerates to a velocity `v_(0)` relative to the double-boat system, the two boats accelerate to the left.
`V_(C )("to right")+v_(A)("to left")=v_(0)`
`Mv_(C )=2Mv_(A)`
Solving, we find `v_(A)=(mv_(0))/(m+2M)`, `v_(C )=(2Mv_(0))/(m+2M)`
After the car brakes to a stop, the tension in the string connecting `A`, `B` becomes zero. Applying We find the velocity of `A`(to right) :
`v'_(A)=(mMv_(0))/((m+M)(2+2M))`