Question

Two cars A and B are 5m long each. Car A is at any instant just behind car B. Car A and B have 54km/hr and 36km/hr speed respectively. How much distance car A has to cover on road to overtake car B.
A) 35 m
B) 30 m
C) 32.5 m
D) 27.5 m

Answer 1

Hint:We will use the concept of relative speed for this problem:
When the objects move in the same direction their relative speed will be subtracted and when the objects move in the opposite directions then their respective speed are added.
We will also use the conversion of units from km/hr to m/s.

Complete step by step solution:
Let’s do the conversion of speeds from km/hr to m/s:
1km =1000m and 1hr = 3600 seconds.
Therefore, 54km/hr$ = 54 \times \dfrac{{1000}}{{3600}}$ m/s (multiplied both the term by their conversion scale)
$ = 54 \times \dfrac{5}{{18}} = 15$m/s
Similarly for 36km/hr
$
   = 36 \times \dfrac{{1000}}{{3600}} \\
   = 10m/s \\
 $
As both cars are moving in the same direction, we will subtract the two speeds to find the relative speed between the two.
Relative speed = 10 -5 =5 m/s
Car A is just behind car B and each of the two are 5m each so the total distance becomes 10m for car A to overtake car B.
Time taken by car A to overtake car B is:
$
   \Rightarrow t = \dfrac{d}{s} \\
   \Rightarrow t = \dfrac{{10}}{5} = 2 \\
 $ ( time is equal to the ratio of distance and speed)
Time taken by car A to overtake car B is 2s, while on the road it is
Actual speed of car A is 15m/s and time is 2s;
Then, distance on road =2$ \times $ 15=30m

Option 2 is correct.

Note:Relative speed is defined as the speed of a moving body with respect to another. When a train is moving, the person sitting inside the train is also moving with respect to the person who is standing on the platform but in reference to the train the man sitting inside it is at rest. This concept of reference and relative speeds.