Initially, trucks A and B are travelling in opposite directions. A has mass 1000 kg and is travelling at speed 7ms^-1. B has mass 4000kg and is travelling at speed 2ms^-1. What is their speed and direction after collision if they move together?

The law of conservation of momentum states that for a system, under the influence of no external forces, the sum of the momenta of all objects, which are calculated by multiplying their masses and velocities, in the system is conserved. It is important to note that momentum is calculated using the velocity of objects and not their speed and thus accounting for the direction that objects are travelling in is vital. Firstly, we must choose what direction positive velocities will be in and we can choose the direction that truck A is initially travelling. Therefore, since trucks A and B are travelling in opposite directions truck B initially has negative velocity. The total momentum of the system is 1000kg7ms^-1+4000kg-2ms^-1=-1000kgms^-1 and this will be conserved. After the collision, trucks A and B move together and thus will have a combined mass of 1000kg+4000kg=5000kg and will have momentum of 5000kgv, where v is theircommon velocity. Hence, -1000kgms^-1=5000kgv which gives the result v=-0.2ms^-1. Finally, since the velocity is negative then that means they move together in the direction that truck B was initially travelling in, with speed 0.2ms^-1.