If a vehicle A, 1000kg moving at 5m/s collides with vehicle B, 750kg, moving in the opposite direction at 8m/s assuming no rebound what is the velocity of the vehicles after collision.

for this question we must consider the conservation of momentum law which states that the total momentum in a system before a collision must equal the total momentum in a system after a collision where momentum=mass x velocity. i.e m1u1+m2u2=m1v1+m2v2 where u= initial velocity, v= final velocity and m=mass.so far we know; vehicle A-> m=1000kg and u=5m/s vehicle B-> m=750 kg and u=-8m/s (best to draw a diagram of initial directions of vehicles to illustrate sign conventions) assume positive direction is the direction of vehicle A illustrated as to the right.The question states that we should assume there is no rebound, this means that we are to assume that the two vehicles combine in the collision and move off in the same direction at the same velocity, v, with a combined mass of 1750kg.we can then substitute our values into the momentum equation to find v.(1000x5)+(750x-8)=1000v+750v , 1000v+750v factorises as 1750vtherfore, 1750v=5000-6000=-1000so v=-1000/1750= -0.57m/s (to left)