A cart of mass 0.400 kg moves with a speed of 1.2 m/s toward a secondary cart of mass 0.300 kg that is initially at rest. When the carts collide they stick together. What speed do the carts move with after the collision

0.686 m/s

Explanation:

The principle of conservation says the sum of momenta before collision is equal to the sum of momenta after collision in an isolated system. Here, we assume the system is not acted upon by any external force.

The initial momentum = momentum of 1 st cart + momentum of 2nd cart

                                     = 0.400 × 1.2 + 0.300 × 0 = 0.48 kg m/s

The final momentum = (0.400 + 0.300) × v   (since they stick together)

0.700 v = 0.48

v = 0.686 m/s

Initial velocity, U = 4.5m/s

Explanation:

Given the following data;

Final velocity, v = 12m/s

Time, t = 5 seconds

Acceleration, a = 1.5m/s²

To find the initial velocity, we would use the first equation of motion.

Where;

V is the final velocity.

U is the initial velocity.

a is the acceleration.

t is the time measured in seconds.

Substituting into the equation, we have;

12 = U + 1.5*5

12 = U + 7.5

U = 12 - 7.5

Initial velocity, U = 4.5m/s