Relative Speed MCQ Quiz - Objective Question with Answer for Relative Speed - Download Free PDF

Calculation

Car A speed = 72 km/h

Car B speed = 54 km/h

They are moving in opposite directions

Distance between them = 693 km

They meet after t hours

When two objects move in opposite directions, their relative speed is the sum of their speeds:

Relative Speed = 72 + 54 = 126 km/h

Time = [Distance/Relative Speed] = 693/126 = 5.5 hours

So, t + 2.5 = 5.5 + 2.5 = 8 

Calculation

Speed of Train E is 25% greater than Train B

→ Speed of E = 1.25B

Speed of Train F is 25% greater than Train A

→ Speed of F = 1.25A

Sum of speed of Train A and B = 108 km/h

→ A + B =108

Trains E and F cross each other in 96 seconds while moving in opposite directions

Ratio of lengths of E : F = 3 : 2

→ Let lengths be: E = 3x, F = 2x

→ So total distance to cross = 5x

Time = 96 seconds

So, (A + B) =108 ---------Equation (1)

Then:

Speed of E = 1.25b

Speed of F = 1.25a

So relative speed when they cross each other =

[1.25a + 1.25b] = 1.25(a + b) =1.25 × 108 = 135 km/h = [135 × [5/18] = 37.5 m/s

Distance=Speed × Time = 37.5 × 96 = 3600 meters

But distance = E + F = 5x

So, 5x=3600

⇒ x = 3600 / 5 = 720

Train F = 2x = 2 × 720 = 1440 meters

Calculation:

Robber takes 12 steps while the guard takes 9 steps in the same time.

This means the step frequency ratio steps per unit time is:

Guard Steps:Robber Steps = 9 : 12 = 3 : 4

4 steps of the guard = 5 steps of the robber in distance.

Thus, the step length ratio is:

Guard Step Length:Robber Step Length = 5:4

Speed is determined by step frequency × step length.

Let:

Guard’s step frequency = 33 steps/sec.

Robber’s step frequency = 44 steps/sec.

Guard’s step length = 55 units.

Robber’s step length = 44 units.

Guard’s Speed = 3 × 5 = 15 units/sec.

Robber’s Speed = 4 × 4=16 units/sec.

Speed Ratio = Guard’s Speed:Robber’s Speed = 15 : 16

Thus, the ratio of the speeds of the guard and the robber is 15 : 16.

Given:

Ratio of speeds of two trains = 7:8

Speed of the second train = 400 km in 4 hours = 400 / 4 = 100 km/h

Formula Used:

If the ratio of speeds of two trains is a:b, then:

Speed of the first train = (Speed of the second train × a) / b

Calculation:

Given ratio = 7:8, Speed of the second train = 100 km/h

Speed of the first train = (100 × 7) / 8

⇒ Speed of the first train = 700 / 8

⇒ Speed of the first train = 87.5 km/h

The speed of the first train is 87.5 km/h.

Given:

Speed of train from A = 70 km/h

Speed of train from B = 60 km/h

Time = 11/2 hours

Distance between them after 11/2 hours = 65 km

Formula Used:

Distance = Speed × Time

Relative Speed = Speed₁ + Speed₂ (when moving towards each other)

Calculation:

Distance covered by train from A in 11/2 hours = 70 × 11/2 =  385 km

Distance covered by train from B in 11/2 hours = 60 × 11/2 = 330 km

Total distance covered by both trains = 385 + 330 = 715 km

Total distance between station A and B = Distance covered + Distance remaining

Total distance between station A and B = 715 + 65 = 780 km

Relative speed of the trains = 70 + 60 = 130 km/h

Time to cross each other = Total distance / Relative speed

⇒ Time = 780 / 130 = 6 hours

∴ The trains would cross each other after 6 hours of starting.

Given:

Total track length = 1200 m

Speed of A = 2 m/s ; speed of B = 4 m/s

Speed of C = 6 m/s

Formula used:

Distance = relative speed × time

Calculation:

Relative speed of A and B = (4 - 2) = 2 m/s

Relative speed of B and C = (6 + 4) = 10 m/s

Relative speed of A and C = (6 + 2) = 8 m/s

Time taken by A and B = 1200/2 = 600 sec

Time taken by B and C = 1200/10 = 120 sec

Time taken by A and C  = 1200/8 = 150 sec

A, B and C will meet at = L.C.M {600,120, 150} = 600 sec = 600/60 = 10 minutes

∴ The correct answer is 10 minutes.

Concept used:

Speed × time = distance

Calculation:

In the 1^st 20 min the thief cover distance = 4 m,

20 min in hour = 20/60 hour

Let's assume that the speed of security guard = x m/hr, where x > 12

According to the question,

⇒ (x - 12) × 20/60 = 4

⇒ x - 12 = 12

⇒ x = 24

∴ The correct answer is 24 m/h

Given,

Sathish completes 900 m race.

Kiran covers = 900 – 270 = 630 m

Rahul covers = 900 – 340 = 560 m

⇒ Ratio of their speed = 630/560

When Kiran covers 900 m race  then

⇒ Rahul would cover = 900 × 560/630 = 800 m

Given:

A and B start running on a circular track (length 400 m) from the same point simultaneously with speeds of 10 m/s and 16 m/s

Formula used:

Time = \(\dfrac{distance}{speed}\)

Calculations:

A takes time to complete one round = 400/10 = 40 sec

B takes time to complete one round = 400/16 = 25 sec

Both will meet at the starting point = LCM of 40, 25

Required time = LCM = 5 × 5 × 8 = 200 secs

∴ The answer is 200 seconds.

Given:

Distance between constable and thief = 200 m

Speed of constable = 8 km/h

Speed of thief = 6 km/h

Formula used:

Distance = relative speed × time

Calculation:

Distance = relative speed × time

⇒ 200 = (8 - 6) × (5/18) × time

⇒ 200 = 2 × (5/18) × time

⇒ Time = (200 × 18)/10

⇒ Time = 360 sec

Distance covered by thief = 6 × (5/18) × 360

⇒ 6 × 100 = 600 m

∴ The correct answer is 600 m.

GIVEN:

At a distance of 225 m policeman spotted  a thief

speed of the thief  is 11km/h

speed of policeman is 13 km/h :

CONCEPT USED:

Relative speed when the thief and policeman are running in the same direction =  ( speed of policeman - speed of the thief) 

Distance = Speed × Time 

CALCULATION :

Relative speed = ( 13 - 11 ) = 2 km/h

To convert km/h into m/s we have to multiply it by 5/18.

⇒ 2 × 5/18 = 5/9 m/s.

\(Time = \frac{Distance}{Speed}\)

⇒ Time = \(\frac{225}{(5/9)}\) = 225 × \(\frac{9}{5}\) =  405 seconds.

The distance thief had run before he was caught by the policeman 

⇒ 11× \(\frac{5}{18}\)× 405 =  1237.5 m

∴ The distance thief had run before he was caught by the policeman is 1237.5 m

Given : 

Speed of 1st person = 9 m/s

Speed of the 2nd person = 6 m/s

Circumference of the Track = 1800 m

Concept used :

Speed = Distance covered / Time taken

Calculation :

The time taken by the first person to complete a full lap is 1800 m / 9 m/s = 200 seconds.

​The time taken by the second person to complete a full lap is 1800 m / 6 m/s = 300 seconds.

​The LCM of 200 seconds and 300 seconds is 600 seconds, which means they will end up in the same initial positions after 600 seconds.

​Let the two persons cross each other for the first time after x seconds.

Then, total distance covered by 1st person = 9x and the 2nd person = 6x

Now, the total distance covered by both the person = Circumference of the track

⇒ 9x + 6x = 1800m ⇒ 15x = 1800m ⇒ x = 120 s

∴ The two persons will cross each other for the first time after 120 seconds.

The two persons will cross each other again after 120 seconds, and then again after 120 seconds, and so on.

So in 600 seconds, they will meet = 600/120 = 5 times

Therefore, the two persons will cross each other at 5 distinct points on the track.

Shortcut Trick

S1 = 9 m/s and S2 = 6 m/s 

S1/S2 = 3/2

They are running in opposite directions so they will meet each other at distinct points = 2 + 3 = 5 

Let speed be x km/hr

So, distance between stations = 10x km

When trains are travelling in opposite direction, relative speed = 2x km/hr.

Train A leaving at 5 am and train B at 7 am,

⇒ Distance travelled by A in 2 hrs = 2x

⇒ Remaining distance = 10x - 2x = 8x

⇒ Meeting time = 8x/2x = 4 hrs

Given:

Distance between policeman and thief in the starting = 300 m

Speed of policeman = 9 km/hr

Speed of thief = 8 km/hr

Concept: /Formula:

If the speed of a policeman and thief is x km/hr and y km/hr, then

Relative speed, if same directions = (x – y) km/hr

Distance between them after n hrs = (x – y) × n

1 km/hr = 5/18 m/sec

1 min = 60 sec

Calculation:

3 min = 3 × 60 = 180 seconds

Distance between policeman and thief in starting = 300 m

Relative speed of policeman and thief, if same directions = (9 – 8) = 1 × (5/18) = (5/18) m/sec

Distance covered in 180 seconds = (5/18) × 180 = 50 m

Distance between them after 180 seconds= 300 – 50 = 250 m

∴ Distance between them after 3 min is 250 m.

Given

Circular race length: 5000 m

Speed of A: 36 km/h (or 10 m/s)

Speed of B: 54 km/h (or 15 m/s)

Concept:

Time = Distance/Speed. In opposite directions, the speeds add up; in the same direction, they subtract.

Solution:

Time taken when running in opposite directions = 5000/(10 + 15) ⇒ 200 seconds

Time taken when running in the same direction = 5000/(15 - 10) ⇒ 1000 seconds

The difference in times = 1000 - 200 ⇒ 800 seconds

Therefore, the difference between the times taken to meet for the first time in opposite and the same directions is 800 seconds.