Motion Test

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Motion Test - 57

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Question 1
1 / -0

A boy having uniform acceleration of $$\displaystyle 10\ { m s }^{ -2 }$$ has a velocity of $$\displaystyle 100\ { ms }^{ -1 }$$. In what time the velocity will be doubled?

A
$$8\ s$$

B
$$10\ s$$

C
$$12\ s$$

D
$$14\ s$$

Solution

Initial velocity $$u = 100$$ $$ms^{-1}$$
Final velocity $$v = 200$$ $$ms^{-1}$$
Acceleration of the boy $$a = 10$$ $$ms^{-2}$$
Using , $$v = u+ at$$
$$\therefore$$ $$200 = 100 + 10 t$$
$$\implies$$ $$t = 10$$ $$s$$
Question 2
1 / -0

Uniform linear motion is a/an _______ motion while uniform circular motion is a/an _______ motion.

A
accelerated, non accelerated

B
non accelerated, accelerated

C
deviated, retarded

D
uniform, retarded

Solution

In a uniform linear motion, the direction of motion is fixed and since it also has a constant speed, uniform linear motion is not accelerated. In a uniform circular motion, the direction of motion changes continuously. So even if it has a constant speed, it is accelerated.
Question 3
1 / -0

Which of the following statement must always be true?
I.If an objects acceleration is zero, then its speed must remain constant.
II. If an objects acceleration is constant, then it must move in a straight line.
III. If an objects speed remains constant, then its acceleration must be zero.

A
I and II only

B
I and III only

C
I only

D
III only

E
II and II only

Solution

Acceleration is the rate of change of speed of the object. Thus when acceleration is zero, the speed of object remains constant.

Acceleration of an object moving in a circular path is $$\dfrac{v^2}{R}$$. Thus an object with constant acceleration may not move in a straight line.

Again in case of circular path, the speed remains same, but acceleration is finite.
Question 4
1 / -0

A block is moving in a circular path at constant speed. Which of the following statements is/are true?
I. The velocity is constant.
II. The direction of motion is constant.
III. The magnitude of velocity is constant.

A
II only

B
I and III only

C
II and III only

D
I and II only

E
III only

Solution

In a circular motion of the block, the direction of velocity is changing so it is not constant. As the direction of velocity keeps changing, the direction of motion also keeps changing but the magnitude of velocity i.e., its speed remains constant.
Question 5
1 / -0

Velocity, being a vector quantity, positive velocity means

A
that the body is moving away from the reference point

B
that the body is moving towards the reference point

C
that the body is stationary

D
nothing specifically

Solution

Displacement is measured from a reference point in an outward direction to a position of the body.
So, positive displacement indicates that the body moves away from the reference point.
Thus, positive velocity indicates rate of change of positive displacement, or change of displacement in a direction away from the reference point.
Question 6
1 / -0

The slope of displacement-time graph being negative implies

A
that the object moves towards the reference point

B
that the object moves away from the reference point

C
that the object is stationary

D
none of these

Solution

Negative slope of a displacement-time graph indicates negative velocity.
Velocity is measured negative when a body moves towards the reference point.
Question 7
1 / -0

An object of mass m moving with constant speed $$v$$ completes one round of circular path. Three conditions are given below, which one of the following statements is correct
I. The displacement is zero.
II. The average speed is zero.
III. The acceleration is zero

A
I only

B
I and IIonly

C
I and III only

D
III only

E
II and III only

Solution

After one complete rotation, the object comes back to its initial position.
Thus the displacement of the object is zero.
Acceleration of the object $$a = \dfrac{v^2}{r} \neq 0$$
Also the distance covered by object in one rotation in time $$t$$ $$D = 2\pi r$$
Average speed $$ = \dfrac{D}{t} = \dfrac{2\pi r}{t} \neq 0$$
Thus option A is correct.
Question 8
1 / -0

A car accelerates uniformly so that it goes from a velocity of $$20 {m}/{s}$$ to a velocity of $$40 {m}/{s}$$ in $$5$$ seconds. Find out the acceleration of a car?

A
$$0.2 {m}/{{s}^{2}}$$

B
$$4 {m}/{{s}^{2}}$$

C
$$5 {m}/{{s}^{2}}$$

D
$$10 {m}/{{s}^{2}}$$

E
$$80 {m}/{{s}^{2}}$$

Solution

Given : $$u = 20$$ m/s $$v = 40$$ m/s $$t =5$$ s
Using $$v = u+ at$$
$$\therefore$$ $$40 = 20 + a (5)$$ $$\implies a = 4$$ $$m/s^2$$
Question 9
1 / -0

A car accelerates steadily so that it goes from a velocity of 20 m/s to a velocity of 40 m/s in 4 seconds. What is its acceleration?

A
0.2 $$m/s^2$$

B
4 $$m/s^2$$

C
5 $$m/s^2$$

D
10 $$m/s^2$$

E
80 $$m/s^2$$

Solution

Given,
$$u=20\ m/s\\v=40\ m/s\\t=4\ sec$$

Acceleration is a measure of the change in velocity over time.
Change in velocity is $$\Delta v=v-u$$
$$\Delta v=40m/s-20m/s=20m/s$$
Since this change in velocity takes place over 4 seconds,
Car acceleration is $$a=\dfrac{\Delta v}{\Delta t}$$

$$a=\dfrac{20m/s}{4s}=5m/s^2$$
Question 10
1 / -0

The graphs below the position versus time for three differences cars 1, 2 and 3. Rank these cars according the magnitudes of their velocities at the time "t" indicated on the graph, greatest first

A
1, 2 , 3

B
1, 3 , 2

C
2, 1, 3

D
3, 2, 1

E
3, 1, 2

Solution

Slop of Potion time graph $$M=\dfrac{\text{Change in possion}}{\text{Time taken}}=Velocity$$

In a position-time graph, velocity is given by the slope of position curve with time axis. from the given graph, it is clear that car 2 has the maximum slope with time axis at time $$t$$, then car 1 and as the slope of car 3 is zero with time axis therefore its velocity is zero i.e. it is stationary. the rank is $$2,1,3$$.

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Re-Attempt Weekly Quiz Competition

Motion Test - 57

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Motion Test - 57

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Question 1

$$8\ s$$

$$10\ s$$

$$12\ s$$

$$14\ s$$

Solution

Question 2

accelerated, non accelerated

non accelerated, accelerated

deviated, retarded

uniform, retarded

Solution

Question 3

I and II only

I and III only

I only

III only

II and II only

Solution

Question 4

II only

I and III only

II and III only

I and II only

III only

Solution

Question 5

that the body is moving away from the reference point

that the body is moving towards the reference point

that the body is stationary

nothing specifically

Solution

Question 6

that the object moves towards the reference point

that the object moves away from the reference point

that the object is stationary

none of these

Solution

Question 7

I only

I and IIonly

I and III only

III only

II and III only

Solution

Question 8

$$0.2 {m}/{{s}^{2}}$$

$$4 {m}/{{s}^{2}}$$

$$5 {m}/{{s}^{2}}$$

$$10 {m}/{{s}^{2}}$$

$$80 {m}/{{s}^{2}}$$

Solution

Question 9

0.2 $$m/s^2$$

4 $$m/s^2$$

5 $$m/s^2$$

10 $$m/s^2$$

80 $$m/s^2$$

Solution

Question 10

1, 2 , 3

1, 3 , 2

2, 1, 3

3, 2, 1

3, 1, 2

Solution

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