Relative Speed | MCQs

Explanation

Given:

• Length of each train = 150 m

• Total length to cross = 150 m + 150 m = 300 m

• Time taken to cross = 15 seconds

• Trains are moving in opposite directions at the same speed

 Step 1: Use the formula

Relative speed= Total distance/Time ​= 300 / 15​ = 20 m/s

Since both trains have the same speed and are moving in opposite directions:

Relative speed=v+v=2v=20 m/s⇒v=20​/2=10 m/s

Step 2: Convert to km/h

$$1 text{m/s} = 3.6 text{km/h} Rightarrow 10 text{m/s} = 10 times 3.6 = 36 text{km/h}$$

Explanation

Let the speed of the slower friend be $x$ km/h, then the speed of the faster friend is$x+2$ km/h.

After 1 hour, their total distance apart is the sum of their speeds:

$$x+(x+2)=10$$

Simplifying:

2x+2=10

$$2x=8\Rightarrow$$x=4km/h

So, the slower friend's speed is 4 km/h, and the faster friend's speed is $4 + 2 = 6$ km/h.

Explanation

 7t

First person distance traveled in time t = 28

 laps = 1

4 laps 

 Distance covered by the second person at time t = 38

 laps 

 First-person speed = 14t

 Second-person speed = 38t

 The two  start from A and B respectively, so they  meet  when there is a difference of 78

 laps. 

 Relative velocity of A and B: 

 = (38t-14t) = 18t

 Time  to complete 78

 laps at this speed: 

 = (78 × 8t) = 7t

Explanation

When the trains move in opposite directions, their relative speed is the sum of their individual speeds:

60 km/h + 40 km/h = 100 km/h

To convert this to meters per second, divide by 3600 (since there are 3600 seconds in an hour):

100 km/h ÷ 3600 = 27.78 m/s (approximately)

The total distance covered by the trains as they cross each other is the sum of their lengths:

140 m + 160 m = 300 m

Time = Distance ÷ Relative Speed

Time = 300 m ÷ 27.78 m/s ≈ 10.8 s

Explanation

Explanation

Let Speed of the man is x kmph.

Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20 + x) kmph.

Or, 20×1060=860×(20+x)

Or, 200 = 160 + 8x

Or, 8x = 40

Hence, x = 5kmph

Explanation

Let the speed of the train be x km/h and the speed of the car be y km/h.

Case 1: He travels 120 km by train and the rest (480 km) by car, taking 8 hours in total.

Time taken by train = Distance / Speed = 120 km / x km/h = 120/x hours

Time taken by car = Distance / Speed = 480 km / y km/h = 480/y hours

Total time = 8 hours = (120/x) + (480/y)

Case 2: He travels 200 km by train and the rest (400 km) by car, taking 8 hours 20 minutes (or 8.33 hours) in total.

Time taken by train = Distance / Speed = 200 km / x km/h = 200/x hours

Time taken by car = Distance / Speed = 400 km / y km/h = 400/y hours

Total time = 8.33 hours = (200/x) + (400/y)

Now, we have two equations and two variables. Solving them simultaneously, we get:

x = 60 km/h (speed of the train)

y = 80 km/h (speed of the car)

Explanation

When objects move in opposite directions, relative speed = sum of speeds.
=> 60 + 135 = 195 Kmph