Question

A 2.0-kg cart collides with a 1.0-kg cart that is initially at rest on a low-friction track. After the collision, the 1.0-kg cart moves to the right at 0.50 m/s and the 2.0-kg cart moves to the right at 0.25 m/s . If the positive direction is to the right, what was the initial velocity of the 2.0-kg cart?

Answer 1

Initial velocity of first cart will be 0.5 m /sec

Step-by-step explanation:

We have given mass of the cart
`m_1=2kg`

Its collides with other cart of mass
`m_2=1kg`

Let the initial velocity of cart 1 is
`v_(1i)`

As the car 2 is initially at rest so
`v_(2i)` = 0 m/sec

After the collision velocity of first cart is 0.25 m/sec

So
`v_(1f)` = 0.25 m/sec and velocity of second cart is 0.50 m /sec

So
`v_(2f)` = 0.5 m/sec

From conservation of momentum we know that

`m_1v_(1i)+m_2v_(2i)=m_1v_(1f)+m_2v_(2f)`

`2* v_(1i)+1* 0=2* 0.25+1* 0.5`

`v_(1i)` = 0.5 m /sec

So initial velocity of first cart will be 0.5 m /sec