Question

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

Answer 1

The distance between car A and car B = 100 m
Therefore, For car A the distance must be 100m more than car B's distance tobe at same distance.

Speed of car A = 10 m/s
Speed of car B = 5 m/s

If car A and car B travel 10 sec each
Then distance travelled by car A = 100m
distance travelled by car B = 50m
The difference between the two cars is half of required (100 m)

Therefore, double the time
That is, time = 20 sec
Then distance travelled by car A = 200m
distance travelled by car B = 100m
The difference between the two cars is 100m
So we can say that two cars are at same distance.

Now we have to calculate their distances just more than 20 sec
Try time = 20.1 sec
Then distance travelled by car A = 201 m
distance travelled by car B = 20.5 m

Therefore, car A overtake car B at 201 m