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QUESTION: 1

The displacement of a particle is given by x = (t – 2)^{2} where x is in meters and t in seconds. The distance covered by the particle in the first 4 seconds is:

Solution:

**► **Displacement at t = 0 sec is: x = 4 meters

**► **Displacement at t = 2 sec is: x = 0 meters

**► **Displacement at t = 4 sec is: x = 2^{2} = 4 meters

∵ Particle changes direction at t = 2s

⇒ Particle travels from x = 4 m to x = 0 m in the first 2 sec and then from x = 0 m to x = 4 m position in the next two seconds

Distance travelled = 8 meters.

QUESTION: 2

The ratio of displacement to distance is:

Solution:

As the magnitude of displacement always either less than or equal to distance travel. Hence, the numerical ratio of displacement to distance is either less than or equal to 1.

QUESTION: 3

A vehicle travels half the distance L with speed V_{1}and the other half with speed V_{2}, then its average speed is

Solution:

Let the vehicle travels from A to B. Distances, velocities, and time taken are shown. To calculate average speed we will calculate the total distance covered and will divide it by the time interval in which it covers that total distance.

Time taken to travel first half distance t_{1}

Time taken to travel first half distance t_{1}

Total time taken = t_{1 }+ t_{2}

We know that v_{av }= Average speed = Total Distance / Total Time

QUESTION: 4

Which of the following statements about distance is true?

Solution:

**Displacement **is the net distance between the initial position and final position, while the **distance** is the measure of the total path traveled during the entire journey.

**Thus, distance is always equal to or more than displacement.**

*Multiple options can be correct

QUESTION: 5

Which of the following quantity remains constant during the uniform circular motion?

Solution:

In a uniform circular motion, the direction of velocity changes but its magnitude remains constant, hence, speed remains constant in a uniform circular motion.

QUESTION: 6

The magnitude of average velocity is equal to the average speed if the motion of an object is along a straight line and in the same direction.

Solution:

The magnitude of the average velocity of an object is equal to its average speed, only in one condition **when an object is moving in a straight line**.

QUESTION: 7

A particle is moving along a circle of radius R such that it completes one revolution in 40 seconds. What will be the displacement after 2 minutes 20 seconds?

Solution:

**► **1 revolution in 40 seconds

**► **In 1 second it covers = 1/40 revolution

**► **In 140 sec = 1/40 * 140 =7/2 rotation = 3 and half rotation

Displacement = R + R = 2R [∵ the particle will be on the diametrically opposite end]

QUESTION: 8

The numerical ratio of velocity to speed is:

Solution:

When an object is moving along a straight path, magnitude of average **velocity** is equal to the average **speed**. Therefore, **numerical ratio** of average **velocity** to average **speed is** one in a straight line motion.

But, during curved motion, the **displacement < distance covered**, so the **velocity < speed.**

QUESTION: 9

Two escalators move people up and down between floors of a shopping mall at the same rate, either up or down. What of the following statements regarding the motion of the escalators is true?

Solution:

As the particles are moving at the same rate, their speed is the same but **velocities will be different beacuse their directions will be different.**

QUESTION: 10

A coordinate system that enables us to describe the position of a body in space at any instant of time is called:

Solution:

Reference frame, also called frame of reference, in dynamics, system of graduated lines symbolically attached to a body that serve to describe the position of points relative to the body.

QUESTION: 11

The displacement of a particle starting from rest (at t = 0) is given by s = 6t^{2}-t^{3 }. The time in seconds at which the particle will attain zero velocity again, is

Solution:

**► **v = ds/dt = 12t - 3t^{2}

**► **0 = 3t (4 - t)

⇒ t = 0 or 4

Here t = 0 is not realistic so at t = 4 the velocity will be zero.

QUESTION: 12

The displacement of an object may be:

Solution:

The displacement is a relative term, therefore it can be positive, negative or even 0 depending upon the initial position.

QUESTION: 13

If a body does not change its direction during the course of its motion, then ______.

Solution:

Since the object does not change its direction it means that the object is traveling in a straight line.

⇒ The path length and displacement will be equal.

QUESTION: 14

36 km/h is equal to:

Solution:

QUESTION: 15

The ratio of magnitude of velocity and speed is always:

Solution:

The displacement of the body at any given time is always equal to or less than the distance covered.

∵ Velocity is displacement per unit time and speed is the distance covered per unit time.

∴ The ratio of the magnitude of velocity and speed is always **equal to or less than one**.

QUESTION: 16

Suppose our school is 1 km away from our house, and we go to school in the morning, and in the afternoon we come back. Then, the total displacement for the entire trip is:

Solution:

The displacement is 0 because the initial and final position are the same, i.e. the home, and hence, displacement is 0.

QUESTION: 17

An object is in uniform motion along a straight line if it:

Solution:

Uniform motion means regular or equal motion. Thus uniform motion is obtained when an object travels an equal distance in equal intervals of time.

QUESTION: 18

A man starts from his home with a speed of 4 km/h on a straight road up to his office 5 km away and returns to home, then the path length covered is:

Solution:

5 km while going and 5 km while coming back.

⇒ Total path travelled = 10 km

QUESTION: 19

A car covers a distance of 5 km in 5 mins, its average speed is equal to:

Solution:

5 km in 5 mins, which means 1 km in 1 min

Hence, it will travel 60 km in 60 mins, i.e. speed = 60km/hr

QUESTION: 20

Which of the following is not an example of a rectilinear motion?

Solution:

**Rectilinear motion** is another name for straight-line **motion**.

A body is said to experience **rectilinear motion** if any two particles of the body travel the same distance along two parallel straight lines.

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