Question

In a physics experiment, two carts of mass 1.5 kg each are rolled towards each other. The orange cart has a velocity of 2 m/s and the blue cart has a velocity of -1m/s. The carts stick together when they collide. Calculate their final speed. 1 m/s 0.5 m/s 0.33 m/s 0.67 m/s

Answer 1

This is a problem of momentum conservation. So the linear momentum before the collision and the linear momentum after the collsion should be equal, that is to say, that the momentum of the whole system is conserved.

Therefore, One does not need the vector sign here, since the above problem is purely one dimensional in nature.

Pinitial Pfinal

The intial momentum is, $p_{\text{initial}} = m_1 v_1 + m_2 v_2 = \frac32 \cdot 2 - \frac32 \cdot 1 ~ m^2/s = \frac32 ~ m^2/s.$

And the final momentum is, $p_{\text{final}} = m_{\text{final}} v_f = (m_1 + m_2) \cdot v_f = 2 \cdot \frac32 \cdot v_f = 3 \cdot v_f.$

Since the initial and the final momentum must be conserved, so equating,
Pinitial Pfinal
One gets on solving for $v_f,$ $v_f = \frac12 ~ m/s.$

Answer 2

vf=3-1.5/3=2.5m/s

2.5m/s