Question

A cart of mass 2.50 kg moving with a speed of 4.00 m/s collides head-on with a 1.50 kg cart at rest. If the collision is elastic, what will be the speed and direction of each cart after the collision?

Answer 1

m1 = 2.5kg v1i = +4 m/s

m2 = 1.5 kg v2i = 0 m/s

we need v2f and v1f so  

we need to apply momentum and energy collision becuase of collision is elastic

Pi =Pf

m1*v1i+m2*v2i = m1*v1f +m2*v2f  

energy conservation

0.5m1*v1i^2+0.5*m2*v2i^2 = 0.5*m1*v1f^2 +0.5*m2*v2f^2

from these two

we got

v1f = 1 m/s

v2f = 5 m/s

both have the same direction and moving in the same direction in which initially cart of mass 2.5 kg was moving

let me know in a comment if there is any problem or doubts