Motion and Time Test

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Motion and Time Test - 6

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Question 1
1 / -0

A person starts from point A towards point B following a straight path. After touching the point B, he returns to the point A along the same path. During the journey from A to B, he travels at a constant speed of 40 m/s and from B to A, he travels at a constant speed of 60 m/s. What is the average speed for the whole journey?

A
50 m/s

B
48 m/s

C
46 m/s

D
45 m/s

Solution

As average speed = Total distance/Total time
Let the time taken from A to B be t₁ and the time taken from B to A be t₂.
Put AB = d.
Hence, average velocity,

Here,
Question 2
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A motorist drives north for 30 minutes at 50 miles per hour and then stops for 10 minutes. He then continues towards north travelling 20 miles in 20 minutes. What is the average speed for the whole journey (in miles per hour))?

A
70

B
50

C
45

D
60

Solution

Average speed = Total distance travelled/Total time

Total distance travelled =
Total time = 30 min + 10 min + 20 min = 60 min = 1 hr
Question 3
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A person started from point 'O' and travelled 10 km towards east. Then, he turned left and travelled another 8 km. After that, he turned left again and travelled 4 km. He covered the whole journey in 2 hours. What was the average velocity of the person for the whole journey?

A
10 km/hr

B
6.5 km/hr

C
5 km/hr

D
3.25 km/hr

Solution

From the figure we can conclude that OD = 6 km.
Hence, displacement,

Average velocity = Total displacement/Total time
Average velocity = 10/2 = 5 km/hr
Question 4
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A person is moving along a circular path of radius 70 m. If he completes one round in 220 seconds, then the average speed of the person is

A
1 m/s

B
2 m/s

C
7 m/s

D
22 m/s

Solution

Distance covered in one round = 2πr

Average speed = Total distance travelled/total time taken
Question 5
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Which of the following depicts the correct distance-time graph for a stationary body?

A

B

C

D

Solution

For the object at rest, the distance-time graph is a straight line parallel to the time axis.
Question 6
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What can you say about the motion of an object whose distance-time graph is a straight line inclined to the time axis?

A
The object is at rest.

B
The object is moving with uniform speed.

C
The object is moving with variable speed.

D
The object has a increasing speed.

Solution

For the object moving in a straight line, if it covers equal distance in equal time interval, then the object is in uniform motion or moving with constant speed and the distance-time graph is a straight line inclined to the time axis.
Question 7
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Three graphs are shown below. Choose the correct statement from among the following:

A
Only (i) is possible.

B
Only (ii) and (iii) are possible.

C
Only (ii) is possible.

D
All these graphs are possible.

Solution

For the object in motion, the distance travelled by the object cannot be negative and cannot decrease. As the displacement of the object is the change in the position, displacement can be positive or negative.
Question 8
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The distance-time graph for two bodies A and B is shown in the figure below. Which of the following statements is correct?

A
A and B are moving side by side.

B
A is moving faster than B.

C
B is moving faster than A.

D
A is always 20 m behind B.

Solution

The slope of the distance-time graph gives the average speed. The greater the slope of the distance-time graph, the greater is the average speed. Slopes of both bodies are same, so they are moving with same speed. The graph for body A starts from the origin and that for body B starts from 20 m, so A will always be behind B by 20 m.
Question 9
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Consider the distance-time graph shown below:

During which interval does the velocity of the particle become zero?

A
OA

B
AB

C
BC

D
CD

Solution

During the interval AB, the slope of the distance-time graph is zero. So, the object is at rest from A to B.
Question 10
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Consider the two pendulums A and B shown below and choose the correct option showing the relationship between their time periods.

A
Both will have the same time period.

B
A will have longer time period.

C
B will have longer time period.

D
Relation between the time periods cannot be established.

Solution

The time period of a pendulum depends upon the length of the pendulum. The greater the length, the greater is the time period. So, A will have longer time period.
Question 11
1 / -0

Directions For Questions

Directions: Study the following graph and answer the questions based on it.

...view full instructions

What is the distance travelled by the person from the 6^th second to the 8^th second?

A
6 m

B
10 m

C
5 m

D
Zero

Solution

For t = 6 s to t = 8 s, the slope of the graph is zero. Hence, the object is at rest and the distance travelled by the object is zero.
Question 12
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Directions For Questions

Directions: Study the following graph and answer the questions based on it.

...view full instructions

What is the speed of the person for the first 6 seconds?

A
1 m/s

B
2 m/s

C
3 m/s

D
6 m/s

Solution

For the first 6 seconds, the distance travelled by the object is 6 metres.
Hence, average speed,

Question 13

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Karan left his house at 10:00 a.m. for the market. On the way to the market, he stopped to talk to a friend. The distance-time graph for his complete journey is shown below:

Match the statements in Column - I with the values in Column - II:

Column - I	Column - II
A. Distance of the market from Karan's house	P. 2
B. Distance of the point from his house where Karan met his friend	Q. 2.5
C. Average speed of Karan during the whole journey	R. 4
D. Average speed of Karan before he met his friend	S. 5

A - P, B - Q, C - R, D - S

A - Q, B - R, C - S, D - P

A - S, B - P, C - Q, D - R

A - P, B - Q, C - S, D - R

Solution

Distance of the market from Karan's house: 5 km
Distance of the point from his house where Karan met his friend: 2 km
Karan reached the market at t = 12 hours.
Average speed during the whole journey,

He met his friend at t = 10:30 hours.
Hence, average speed of Karan before meeting,
v = Distance travelled/Time taken

Question 14
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Two clocks A and B are shown in the figure below. Clock A has an hour hand and a minute hand, whereas clock B has an hour hand, a minute hand and a second hand. Which of the following statements are correct?

(A) Time interval of 30 seconds can be measured by clock A.
(B) Time interval of 30 seconds can be measured by clock B.
(C) Time interval of 5 minutes can be measured by both the clocks.
(D) Time interval of 4 minutes and 15 seconds can be measured by both the clocks.

A
Only A and D

B
Only A and C

C
Only B and C

D
All of them

Solution

Clock A has an hour hand and a minute hand, whereas clock B has an hour hand, a minute hand and a second hand. So, time interval of 30 seconds can be measured by clock B and time interval of 5 minutes can be measured by both the clocks.
Question 15
1 / -0

Consider the following diagram which shows a pendulum oscillating and its positions at various times.

The time taken by the bob to move from A to C is 1 second and from C to O is 3 seconds. Find the time period of this pendulum.

A
4 s

B
8 s

C
12 s

D
16 s

Solution

The time taken by the bob to move from A to C is 1 second and from C to O is 3 seconds. Hence, the time taken in moving from extreme position to mean position is 4 seconds. Hence, the time period of oscillation is 4 × 4 = 16 seconds.
Question 16
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A man on tour travels the first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the tour?

A
35.55 km/hr

B
37.23 km/hr

C
71.11 km/hr

D
73.47 km/hr

Solution

Total time taken = hr = hr
Average speed = 320 = 71.11 km/hr
Question 17
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A ball moves at 120 metres per second and strikes an object in three seconds. If it moves at the speed of 100 metres per second, how long will it take for the ball to strike the same object?

A
12/5 sec

B
9/5 sec

C
10/5 sec

D
18/5 sec

Solution

Total distance covered by the ball = 120 3 = 360 m
Now, speed of the ball = 100 m/sec
Time taken = = sec
Question 18
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An ant moves from A to B and then to C. What is the magnitude of its displacement?

A
200 m

B
170 m

C
160 m

D
100 m

Solution

An ant moves from A to B and then to C. Then magnitude of its displacement is the shortest distance from point A to C, i.e. AC.

AC =
=
=
=
= 100 m

Hence, option (4) is correct.
Question 19
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The graph below represents

A
motion with uniform speed

B
motion with uniform acceleration

C
motion with non-uniform acceleration

D
motion with non-uniform velocity

Solution

The graph is between position and time (s) whose slope gives us the velocity of a body.
i.e. Velocity of a body = Slope of the position-time graph
Moreover, increasing curve slope of a graph tells that the body covers unequal displacement in equal intervals of time. So, it represents motion with non-uniform velocity.
Hence, option (4) is correct.
Question 20
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A simple pendulum takes 15 seconds to complete 5 oscillations. What is the time period of the pendulum?

A
15 sec

B
5 sec

C
3 sec

D
45 sec

Solution

Time taken to complete one oscillation = 15/5 = 3 sec