Question

Two cars A and B are at positions 100 m and 200 m from the origin at t = 0. They start simultaneously with velocities 10 and 5 m/s respectively. The car A will overtake the car B at a distance of

Answer 1

Given that the car A is at 100 m from the origin and car B is at 200 m.
At t = 0, car A starts with velocity 10 m/s and car B starts with velocity 5 m/s.
Suppose that at a time 't', car A crosses the car B.
Then in time 't' car B has travelled a distance 5t.
Therefore, car A has to travel a distance (200 – 100) = 100m + 5t to cross the car B.
$100+5t=10t$
$\Rightarrow t=\frac{100}{5}=20seconds$
After time = 20 seconds, car A will cross the car B.
Therefore, distance from origin where both car meet $=200+5t=200+5\times 20=300m$.