Question

A 500 g model train car traveling at 0.8 m/s collides with a 300 g stationary car. The cars hook up and move off down the track together. How fast are they going? ( also how do I do it )

Answer 1

0.5 m/s

Explanation:

A 500 g model train car traveling at 0.8 m/s collides with a 300 g stationary car.

Initial velocity of train,
`v_T=0.8\ m/s`

Initial velocity of car,
`v_C=0\ m/s`

Mass of train,
`m_T=500\ g`

Mass of car,
`m_C=300\ g`

The cars hook up and move off down the track together.

Let the final velocity of car and train,
`v_T=v_C=v`

Using conservation of momentum,

Momentum before collision = Momentum after collision

`m_T* v_T+m_C* v_C=(m_T+m_C)* v`

`500* 0.8+300* 0=(500+300)* v`

`v=(400)/(800)`

`v=0.5\ m/s`

Hence, After collision they will going with 0.5 m/s

Answer 2

`0.5ms^(-1)`

Explanation:

Let v be the speed after the collision of both the cars.

Now, momentum is given by: mass × velocity, then by equating the total momentum before and after the collision of the two cars, we get

`500{*}0.8+300{*}0=(500+300)v`

⇒
`400+0=800v`

⇒
`400=800v`

⇒
`v=0.5ms^(-1)`

Thus, they are moving at the velocity of
`0.5ms^(-1)`