Question

# A heavy car $A$ of mass $2000kg$ travelling at $10m/s$ has a head-on collision with a sports car$B$ of mass $500kg$. If both cars stop dead on colliding, what was the velocity of car $B$?

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Solution

## Step 1. Given dataMass of Car $A$, $=2000kg$Speed of Car $A$, $=10m/s$Mass of Car $B$, $=500kg$We need to find speed of Car $B$, ${v}_{B}$Step 2. Formula usedThe linear momentum $P$ of an object is given by$P=mv$where $m$ is the mass of the object and $v$the velocity of the objectStep 3. Find the velocity of the car $B$${m}_{A}=2000kg\phantom{\rule{0ex}{0ex}}{m}_{B}=500kg\phantom{\rule{0ex}{0ex}}{v}_{A}=10m/s$We have to find the velocity of the car $B$ before the collision.After the collision, both cars stop. So after the collision, the velocity of the cars is zero.According to the law of conservation of linear momentum, the sum of linear momentum of the car $A$ and $B$ before the collision is equal to the sum of linear momentum of the car $A$ and $B$after the collision.$\therefore {m}_{A}{v}_{A}+{m}_{B}{v}_{B}=0\phantom{\rule{0ex}{0ex}}⇒{v}_{B}=-\frac{{m}_{A}{v}_{A}}{{m}_{B}}\phantom{\rule{0ex}{0ex}}⇒{v}_{B}=-\frac{2000×10}{500}\phantom{\rule{0ex}{0ex}}⇒{v}_{B}=-40m/s$Hence, the velocity of the car $B$ is $40m/s$.

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