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

Concept:

Relative Velocity in Opposite Directions:

• When two objects are moving in opposite directions, their relative velocity is the sum of their individual velocities.
• Formula for relative velocity, v_rel = v₁ + v₂
• To find the time taken to cross each other, use t = d / v_rel, where d is the total length of both trains.
• Distance traveled by both trains = 30 m + 30 m = 60 m

Calculation:

Given,

Length of each train = 30 m

Velocities: v₁ = 5 m/s, v₂ = 10 m/s

Relative velocity, v_rel = 5 + 10 = 15 m/s

Total distance, d = 30 + 30 = 60 m

Time to cross, t = d / v_rel = 60 / 15 = 4 s

∴ The time taken for the trains to cross is 4 s.
Hence, correct option is 1) 4 s.

Calculation: 

From graph,

\(\rm V_{R G}=15 \sqrt{2} \tan 45^{\circ}\)

⇒ V_RG \(=15 \sqrt{2}\)

⇒ V_RG\(=\frac{30}{\sqrt{2}}\)

∴ The speed of rain drops with respect to the moving girl is \(\frac{30}{\sqrt{2}} \mathrm{kmh}^{-1}\)

Concept:

Average Speed:

• Average speed is defined as the total distance traveled divided by the total time taken.
• It is given by the formula:
• \( v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \)
• In this problem, the vehicle travels half the distance with speed \( \vartheta \) and the remaining half with speed \( 2\vartheta \).
• Speed v" id="MathJax-Element-111-Frame" role="presentation" style="position: relative;" tabindex="0">vv $v$ is defined as the rate at which an object covers distance.
• SI Unit: \( \text{m/s} \)
• Dimensional Formula: \( [M^0 L^1 T^{-1}] \)

Calculation:

Total distance: d

Time for the first half: \(t_1 = \frac{d/2}{v} = \frac{d}{2v}\)

Time for the second half: \(t_2 = \frac{d/2}{2v} = \frac{d}{4v}\)

Total time: \(t = t_1 + t_2 = \frac{d}{2v} + \frac{d}{4v} = \frac{3d}{4v}\)

Average speed: \(\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{d}{\frac{3d}{4v}} = \frac{4v}{3}\)

Conclusion:

∴ The average speed is \(\frac{4v}{3}\) , as shown in option 3.

Concept:

Velocity

• The distance covered by an object in unit time.
• Velocity can be defined as the displacement of the object in unit time.
• SI unit - m/s, Dimensional formula - LT^-1

 Relative Speed

• When two bodies move in opposite directions, then the Relative Speed = Sum of Speeds
• Relative speed is = V_B/A = V_B - V_A

Where, VB = Speed of object B,  VA  = Speed of object A

Calculation:

Here, V_A = 72 km/h = 72 × (5/18) = 20 m/s, towards north

V_B = 72 × (5/18) = 20 m/s = 108 km/h, towards south

Since, V_B/A = VB - VA

 ⇒ - 30 - 20 = - 50

Since, V_g/B = V_g - VB

⇒ 0 - (-30) = 30

Hence Velocity of train B concerning A and the velocity of ground concerning B are -50 and 30.

∴ The correct option is 3)

the answer is C.

Explanation:-

The graph would start at a positive value depicting the initial upward velocity. It then linearly decreases as the object slows due to gravity, reaches zero velocity at its highest point, then becomes negative as the object starts falling back to the ground. Over time, velocity magnitude increases linearly (though velocity remains negative as it's the return phase).

If the entire trip takes 10 seconds, the velocity should reach zero around the 5-second mark.

Mistake Points Velocity is a vector quantity, which means it has both magnitude (speed) and direction. In physics, upward is typically treated as the positive direction, and downward as the negative direction.

Concept;

Equations of Motion

The equations of motion establish the relationship between acceleration, time, distance, initial speed, and final speed for a body moving in a straight line with uniform acceleration.

The equations are

1. v = u + at 
2. \(s = ut + \frac{1}{2}at^2\)
3. v2 = u2 + 2as 

v is final velocity, u  is initial velocity, t is time, a is acceleration, s is the distance travelled.

Calculation:

Given:

v = 50 m/s, a = 2.5 m/s2?

v2 = u2 + 2as 

50² = 2 × 2.5 × s

s = 500 m

Concept:

The initial velocity is the derivative of displacement (S) concerning time (t) at t = 0.

v = dS/dt

Calculation:

We have

⇒ S = 3t² - 5t + 7

⇒ dS/dt = d(3t² - 5t + 7)/dt

⇒ dS/dt = 6t - 5

At t = 0,

⇒ v = 6(0) - 5

⇒ v = -5

∴ Initial velocity is -5.

CONCEPT:

Velocity

• It is defined as the displacement per unit time.
• It is a vector quantity.

\(\Rightarrow v=\frac{dx}{dt}\)

Acceleration

• It is defined as the rate of change of velocity.

\(\Rightarrow a=\frac{dv}{dt}\)

Relative velocity

• It is the vector difference between the velocities of two bodies.

EXPLANATION:

• Since the train is moving at a constant speed, so the horizontal velocity of the man and the coin will be the same even after tossing the coin because there is no acceleration in the horizontal direction.
• So during the whole flight of the coin, the relative velocity in the horizontal direction between the man the coin is zero because the horizontal velocity of the man and the coin is equal.
• So the coin will fall back into his hand. Hence, option 3 is correct.

CONCEPT:

• Relative velocity: The concept of relative velocity occurs when we encounter occasions where one or more objects move in a frame which is non-stationary concerning another observer where the relative velocity is the velocity of an object or observer B in the rest frame of another object or the observer A.
  • In simple terms, velocity is not always a fixed definite quantity it may change from one frame of reference to another.
  • If an object is traveling in a straight line parallel to each other then there exist two cases of relative velocity.

Case 1

• The relative velocity of two objects moving towards each other in opposite direction is given by:

Vrelative = |v1 + v2|

Case 2

• The relative velocity of 2 objects moving in the same direction to each other as given below:

Vrelative = |v1 - v2|

EXPLANATION:

Given that:

Velocity of car (Assume it A) = V_A = 60 km/h

Velocity of man (Assume it B) = V_B = 15 km/h

Both are moving towards each other: Case 1

So Velocity of car with respect to man = V_relative  = |v1 + v2| = 60 + 15 = 75 km/h.

Hence option 4 is correct.

Explanation:

→In the situation of a stationary escalator and moving girl velocity,

\(V=\frac{L}{t_1}\)----(1)

→In the situation of stationary girl and moving escalator velocity,

\(V_1=\frac{L}{t_2}\) -----(2)

→If both escalator and girl keep moving then distance,

L = (V + V₁) t₃   ----(3)

Where t₃ is time to cover that distance when both girl and the escalator keep moving.

Using equations (1), (2), and (3) we get:

Distance, \(L=(\frac{L}{t_1}+\frac{L}{t_2} )\times t_3\)

\(L=L(\frac{1}{t_1}+\frac{1}{t_2} )\times t_3\)

\(1=(\frac{1}{t_1}+\frac{1}{t_2} )\times t_3\)

\(1=(\frac{t_1+t_2}{t_1 \times t_2} )\times t_3\)

Then, time is taken \(t_3=(\frac{t_1 \times t_2}{t_1+t_2} )\)

Hence, option 3 is correct.

Correct option-3

Concept:-

Relative velocity

• Velocity of a moving object with respect to another object either moving or in rest is termed as Relative motion.
• The term relative is actually applied to physical, non-physical, scalar or vector quantities. In fact, all the measurements are relative in physics.
• In relative motion, question are not so complicated as the objects moving with uniform velocities and It is very important to understand many day today events based on it like- Rain man, Boat man problems, velocity of approach, velocity of separation etc.
• In this topic we will consider the velocity with respect to the frame of reference attached to the ground.

For example-

Let us consider two objects, X and Y are moving with velocities V1 and V2 with respect to a common stationary frame of reference, say the ground, a tree or a fixed platform.

The velocity of the object X relative to the object Y can be given as,

V12 = V1 - V2

Similarly, the velocity of the object Y relative to that of object X is given by,

V21 = V2 -V1

From the above two expressions, we can see that

V12 = -V21

Although the magnitude of both the relative velocities is equal to each other.

Mathematically, it is written as-

|V12|=|V21|

Explanation:-

According to question, the velocity of both the bikes are equal.

I.e. the velocity of bike A, = the velocity of bike B = V

Let the direction along with bike A is moving is positive

So, the direction along with bike B is moving is negative.

Now, the relative velocity of bike A with respect to bike B is given as-

VAB = VA - VB

VAB = V-(-V) = 2V  (Because bikes are moving in opposite direction)

Similarly, the relative velocity of bike A with respect to bike B is given as-

VBA = VB - VA

VBA = (-V)-V = -2V

Therefore, we can say that |V12|=|V21|

Hence, option-3 is the correct answer.

Relative velocity concept is used to calculate the velocities of stars and asteroids with respect to earth’s velocity.

The distance between any two things in space can be calculated by the concept of relative velocity.

Some of the engineering applications of relative velocity are

• Mid air fueling of fighter jets
• Launching rockets.
• Speed Detectors.

Concept:

Relative Velocity

• The velocity of one moving body with respect to another object is called relative velocity. 
• It is the vector subtraction of two velocities. 
• The velocity of an object A with respect to another object B is given as 

\(\overrightarrow{V_{AB}} = \overrightarrow{V_{A}} - \overrightarrow{V_{B}} \)

Calculation:

• Given, Rain is falling vertically downward and speed is 5√3 m/s. 
• The velocity of Man is 5 m/s in the east. 
• The unit vector in the downward direction is \(- \widehat{j}\)
• The unit vector in the east direction is \(\widehat{i}\)

We have to here find the relative velocity of rain with respect to man. 

The angle made here is θ with horizontal.

With vertical it is 90 ° - θ 

From the diagram

tan ( θ ) = 5 √3/ 5  =  √3  

We know that tan 60 ° = √ 3 

 θ = 60 °

90 ° - θ = 30 °

So, the angle is 30 ° . (With vertical)

CONCEPT:

• Relative velocity: The concept of relative velocity occurs when we encounter occasions where one or more objects move in a frame which is non-stationary concerning another observer where the relative velocity is the velocity of an object or observer B in the rest frame of another object or the observer A.
  • In simple terms, velocity is not always a fixed definite quantity it may change from one frame of reference to another.
  • If an object is traveling in a straight line parallel to each other then there exist two cases of relative velocity.

Case 1

• The relative velocity of two objects moving towards each other in opposite direction is given by:

Vrelative = |v1 + v2|

Case 2

• The relative velocity of 2 objects moving in the same direction to each other as given below:

Vrelative = |v1 - v2|

EXPLANATION:

Given that:

The velocity of each player = V₁ = V₂ = v

Both players are moving in the opposite direction to each other:

So relative velocity = |v1 + v2| = v + v = 2v

Hence option 3 is correct.

Concept:

If an object is travelling in a straight line parallel to each other then there exist two cases of relative velocity

Case 1

• The relative velocity of 2 objects moving toward or away each other in opposite direction, V _relative is given by:
• v relative = |v1 + v2|

Case 2

• The relative velocity of 2 objects moving along the same direction, V relative is given by v relative = |v1 - v2|

Also, Speed = Distance/Time

Calculation:

Given,

Length of the train = 150 m

Speed of train = 20 m/s East to West

Speed of bird = 5 m/s West to East

Relative Speed of bird w.r.t train = |5 m/s – (-20 m/s)| = 25 m/s

Distance to cover the bird to cross the train = 150 m

We know that,

Time = Distance/Speed

⇒ Time taken by bird to cross the train = \(\frac{{150\;m}}{{25\;m/s}} = 6\;sec\)

CONCEPT:

• Velocity is the rate of change of displacement of the body and is given by

\(\Rightarrow V = \frac{dx}{dt}\)

Where dx = Rate of change in position, dt = change in time

EXPLANATION:

From the triangle

\(\Rightarrow tan 60^{0} = \frac{V_{c}}{V_{R}}\)

\(\Rightarrow V_{R} = \frac{V_{C}}{tan 60^{0}}\)

\(\Rightarrow V_{R} = \frac{20}{\sqrt{3}} = 11.55 m/sec\)

• Hence, option 2 is the answer