Relative Speed
What is Relative Speed?
Relative speed is the rate at which two moving bodies are separating from / coming closer to each other.
OR
It is the speed of one moving body as observed, from the second moving body.
Generally, two cases arise in relative speed.
Objects moving in same direction
Consider two objects A and B separated by a distance of d metres.
If these two objects A and B are moving in the same direction with speeds $S_1$ and $S_2$, then:
Their relative speed = |$S_1$ - $S_2$|
Time needed for them to meet = $\frac{Relative \hspace{1ex} Distance}{Relative \hspace{1ex} Speed}$ = $\frac{d}{|S_1 - S_2|}$ seconds
Q. A bully spotted a boy 150 meters away from him. Both of them started running in the same direction at the same time. If the speeds of the bully and the boy are 3 m/sec and 2 m/sec respectively, then in how much time will the bully catch up with the boy?
Explanation:
Relative speed = 3 – 2 = 1 m/sec (as both are running in the same direction)
Time needed for them to meet = $\frac{Relative \hspace{1ex} Distance}{Relative \hspace{1ex} Speed}$ = 150/1 = 150 seconds (or 2 minutes and 30 seconds)
Q. Two trains of length 300 m each are going in the same direction. If the speeds of two trains are 50 km/hr and 68 km/hr, then in how much time will the faster train completely cross the slower train?
(a) 1 minute 48 seconds
(b) 2 minutes
(c) 1 minute 30 seconds
(d) 3 minutes
Explanation:
When a train crosses another train, the distance travelled is the sum of the length of those two trains.
So, Distance = 300 + 300 = 600 m
When trains are moving in the same direction, then Relative Speed = |Difference of the speeds of those two trains| = (68 - 50) km/hr. = 18 km/hr = 18 × (5/18) m/s = 5 m/s
Time taken = Distance/Speed = 600/5 = 120 seconds = 2 minutes
So, The faster train will cross the slower train completely in 2 minutes.
Answer: (b)
Objects moving in opposite directions
Consider two objects A and B separated by a distance of d metres.
If these two objects are moving in opposite directions with speeds $S_1$ and $S_2$ (either towards each other or away from each other), then:
Their relative speed = $S_1$ + $S_2$
Time needed for them to meet = $\frac{Relative \hspace{1ex} Distance}{Relative \hspace{1ex} Speed}$ = $\frac{d}{S_1 + S_2}$ seconds
Q. A bully spotted another bully 150 meters away from him. Both of them started running towards each other at the same time. If the speeds of the first bully and the second bully are 3 m/sec and 2 m/sec respectively, then in how much time will they meet?
Explanation:
Relative speed = 3 + 2 = 5 m/sec (as both are running towards each other, i.e. in opposite directions)
Time needed for them to meet = $\frac{Relative \hspace{1ex} Distance}{Relative \hspace{1ex} Speed}$ = 150/5 = 30 seconds