Motion in a Straight Line Test 1

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Motion in a Straight Line Test 1

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Question 1
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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:

A
4 m

B
12 m

C
16 m

D
8 m

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 = 2² = 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
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The ratio of displacement to distance is:

A
Greater than 1.

B
Either less than or equal to 1.

C
Less than 1.

D
Equal to 1.

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
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A vehicle travels half the distance L with speed V₁and the other half with speed V₂, then its average speed is

A

B

C

D

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 t₁
Time taken to travel first half distance t₁
Total time taken = t₁+ t₂
We know that v_av= Average speed = Total Distance / Total Time
Question 4
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Which of the following statements about distance is true?

A
It always decreases with time.

B
It can never be less than magnitude of displacement.

C
It cannot be positive.

D
It can be zero.

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.
Question 5
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Which of the following quantity remains constant during the uniform circular motion?

A
Velocity

B
Acceleration

C
Speed

D
Angular Velocity

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
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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.

A
True

B
Can’t Predict

C
False

D
Sometimes true and sometimes false.

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
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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?

A
6R

B
2R

C
4R

D
R

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
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The numerical ratio of velocity to speed is:

A
Either less than or equal to 1.

B
Equal to 1.

C
Greater than 1.

D
Less than 1.

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
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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?

A
The escalators have different speeds and velocities.

B
The escalators have the same velocity, but different speeds.

C
The escalators have the same speed and velocity.

D
The escalators have the same speed, but different velocities.

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

A
Reference frame

B
Intersection point

C
Origin

D
Reference point

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
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The displacement of a particle starting from rest (at t = 0) is given by s = 6t²-t³. The time in seconds at which the particle will attain zero velocity again, is

A
6

B
4

C
2

D
8

Solution

► v = ds/dt = 12t - 3t²
► 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
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The displacement of an object may be:

A
Positive

B
Negative

C
Positive, negative or zero

D
Positive or zero

Solution

The displacement is a relative term, therefore it can be positive, negative or even 0 depending upon the initial position.
Question 13
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If a body does not change its direction during the course of its motion, then ______.

A
Displacement is greater than path length.

B
Path length and displacement are equal.

C
Path length is greater than displacement.

D
Path length is either greater or equal to displacement.

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
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36 km/h is equal to:

A
129. 6 ms^-1

B
600 ms^-1

C
10 ms^-1

D
12.96 ms^-1

Solution
Question 15
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The ratio of magnitude of velocity and speed is always:

A
Equal to or less than one.

B
Less than one.

C
One

D
Equal to or greater than one.

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
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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:

A
1 km

B
2 km

C
-1 km

D
0 km

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

A
Moves equal distances in equal intervals of time.

B
Does not move.

C
Moves equal distances in unequal intervals of time.

D
Moves unequal distances in unequal intervals of time.

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
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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:

A
-5 km

B
5 km

C
0

D
10 km

Solution

5 km while going and 5 km while coming back.
⇒ Total path travelled = 10 km
Question 19
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A car covers a distance of 5 km in 5 mins, its average speed is equal to:

A
1 km/h

B
25 km/h

C
60 km/h

D
None of the above

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

A
A car moving in a circular path.

B
A rain drop falling towards the earth.

C
A car moving on a straight road.

D
A wooden block sliding down the inclined plane.

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.