Class 9 General Science Chapter 8 Motion
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Class 9 General Science Chapter 8 Motion
Answers to Questions Within the Lesson(1)
Q1. An object travels a certain distance. Can its displacement be zero? If yes, give an example in support of your answer.
Ans: Yes, if an object travels a certain distance, its displacement can be zero. For example, if a person starts from a particular point on a circular playground, moves around the playground, and returns to the same starting point, then the displacement will be zero. This is because the initial and final positions are the same. Displacement is the shortest distance between the initial and final positions.
Q2. A farmer walks around the boundary of a square field of side 10 min 40 seconds. What will be his displacement from the starting point after 2 minutes and 20 seconds?
Ans:
Time for one round = 40 seconds
Total time = 2 minutes 20 seconds = 140 seconds
Number of rounds = 140 ÷ 40 = 3.5 rounds
After 3 full rounds, the farmer returns to the starting point. Then he walks half a round more.
In a square field, after half a round from the starting point, the farmer reaches the diagonally opposite corner.
Side of square = 10 m
Displacement = diagonal of square
= v(10² + 10²)
= v200
= 10v2 m ≈14.14 m
So, the displacement from the starting point is 10v2 m (approximately 14.14 m).
Q3. Which of the following statements about displacement are true?
(a) It cannot be zero.
(b) Its value is greater than the distance travelled by the object.
Ans:
(a) False. Because the displacement of an object moving in a circular path can be zero if it returns to the starting point.
(b) False. Because the displacement of an object is always equal to or less than the distance travelled by it.
Answers to Questions Within the Lesson(2)
Q1. Write the difference between speed and velocity.
Ans: The difference between speed and velocity is as below:
Speed:
(i) Speed is the distance travelled by an object per unit time.
(ii) It is a scalar quantity (has only magnitude).
(iii) It does not have any direction.
Velocity:
(i) Velocity is the displacement of an object per unit time.
(ii) It is a vector quantity (has both magnitude and direction).
(iii) It has a definite direction.
Q2. Under what condition(s) is the magnitude of the average velocity of an object equal to its average speed?
Ans: When an object moves along a straight line (in a single direction without changing direction), the magnitude of its average velocity is equal to its average speed.
Q3. What does the odometer of a motor car measure?
Ans: The odometer of a motor car measures the distance travelled by the vehicle.
Q4. What is the path of a uniformly moving object?
Ans: Straight line (rectilinear).
Q5. During an experiment, a signal sent from a spacecraft is received at a ground station in 5 minutes. What is the distance between the spacecraft and the ground station? The signal travels at the speed of light, i.e., 3×108 m/s.
Ans:
Time taken = 5 minutes = 5 × 60 = 300 seconds
Speed of signal = 3 × 108 m/s
Distance = Speed × Time
= 3 × 108 × 300
= 9 × 10¹° m
So, the distance between the spacecraft and the ground station is 9 × 10¹° m.
Answers to Questions Within the Lesson(3)
Q1. When do you say that an object has (i) uniform acceleration and(ii) non-uniform acceleration?
Ans: (i) An object is said to have uniform acceleration when its velocity changes by equal amounts in equal intervals of time.
(ii) An object is said to have non-uniform acceleration when its velocity changes by unequal amounts in equal intervals of time.
Q2. The speed of a bus decreases from 80 km h-¹ to 60 km h-¹ in 5seconds. Find its acceleration.
Ans:
Initial speed (u) = 80 km/h = 80 ×1000/3600 = 22.22 m/s
Final speed (v) = 60 km/h = (60 ×1000/3600 = 16.67 m/s )
Time (t) = 5 s
Acceleration (a) = v – u/t}
= 16.67 – 22.22/5
= -5.55/5
= -1.11 m/s²
So, the acceleration is -1.11 m/s² (retardation).
Q3. A train starts from a station and increases its speed uniformly to 40 km h?¹ in 10 minutes. Find its acceleration.
Ans:
Initial speed (u) = 0
Final speed (v) = 40 km/h = 40 ×1000/3600 = 11.11 m/s )
Time (t) = 10 minutes = 600 s
Acceleration (a) = v – u/t
= 11.11 – 0/600
= 0.0185 m/s²
So, the acceleration is 0.0185 m/s².
Answers to Questions Within the Lesson(4)
Q1. What is the nature of the distance–time graph for uniform and non-uniform motion of an object?
Ans: For uniform motion, the distance–time graph is a straight line.
For non-uniform motion, the distance–time graph is a curved line.
Q2. The distance–time graph of an object is a straight line parallel to the time axis. What can you say about the motion of the object?
Ans: The object is at rest (no motion), because the distance does not change with time.
Q3. The speed–time graph of an object is a straight line parallel to the time axis. What can you say about the motion of the object?
Ans: The object is in uniform motion, as its speed remains constant with time.
Q4. What physical quantity is represented by the area under a velocity–time graph?
Ans: The area under a velocity–time graph represents the displacement of the object.
Answers to Questions Within the Lesson(5)
Q1. A bus starts from rest and moves with an acceleration of 0.1 m/s² for 2 minutes.
(a) Find the speed gained by the bus.
(b) Find the distance travelled.
Ans:
Given, u = 0, a = 0.1 m/s², t = 2 minutes = 120 s
(a) v = u + at
= 0 + (0.1 × 120)
= 12 m/s
(b) s = ut + ½ at²
= 0 + ½ × 0.1 × (120)²
= 0.05 × 14400
= 720 m
Q2. A train is moving with a speed of 90 km/h. Brakes are applied to produce a uniform acceleration of 0.5 m/s². How far does the train move before coming to rest?
Ans:
Initial speed u = 90 km/h = 25 m/s
Final speed v = 0
a = –0.5 m/s²
Using, v² = u² + 2as
0 = (25)² + 2 × (–0.5) × s
0 = 625 – s
s = 625 m
Q3. A trolley moves down an inclined plane with an acceleration of 2cm/s². What will be its velocity after 3 seconds from the start?
Ans:
Given, u = 0, a = 2 cm/s², t = 3 s
v = u + at
= 0 + (2 × 3)
= 6 cm/s
Q4. A car in a race has a uniform acceleration of 4 m/s². How much distance will it cover in 10 seconds from the start?
Ans:
Given, u = 0, a = 4 m/s², t = 10 s
s = ut + ½at²
= 0 + ½ × 4 × (10)²
= 2 × 100
= 200 m
Q5. A stone is thrown vertically upward with a velocity of 5 m/s. If the acceleration during motion is 10 m/s² downward, find the maximum height reached and the time taken to reach that height.
Ans:
Given, u = 5 m/s, v = 0, a = –10 m/s²
Using, v² = u² + 2as
0 = (5)² + 2 × (–10) × s
0 = 25 – 20s
s = 1.25 m
Time, v = u + at
0 = 5 – 10t
t = 0.5 s
So, maximum height = 1.25 m and time taken = 0.5 s.
Exercise: Questions and Answers
Q1. A runner completes one round of a circular track of diameter 200m in 40 seconds. After 2 minutes 20 seconds, what will be the total distance covered and displacement?
Ans:
Diameter = 200 m
Circumference of track = pd = 200p m
Time for one round = 40 s
Total time = 2 min 20 s = 140 s
Number of rounds = 140 ÷ 40 = 3.5 rounds
Distance covered = 3.5 × 200p
= 700p m ≈ 2200 m
After 3.5 rounds, the runner reaches the point opposite to the starting point.
Displacement = diameter = 200 m
Q2. (a) From A to B and (b) from A to C, find Joseph’s average speed and average velocity.
Ans:
In general—
Average speed = Total distance ÷ Total time
Average velocity = Displacement ÷ Total time
Q3. Abdul drives to school at an average speed of 20 km/h and returns by the same route at an average speed of 30 km/h. What is his average speed for the whole journey?
Ans:
Average speed = 2xy/x + y
Here, x = 20 km/h, y = 30 km/h
Average speed = 2 × 20 × 30/20 + 30
= 1200/50
= 24 km/h
Q4. A motorboat on a lake starts from rest and moves in a straight line with a uniform acceleration of 3.0 m/s² for 8.0 seconds. How much distance does it cover during this time?
Ans:
Given, u = 0, a = 3.0 m/s², t = 8 s
s = ut + ½at²
= 0 + ½ × 3 × (8)²
= 1.5 × 64
= 96 m
Q5. A driver of a car moving at 52 km/h applies brakes and the car comes to rest uniformly in 5 seconds. Another driver moving at 3 km/h applies brakes slowly and comes to rest in 10 seconds. Draw the speed–time graph for both cars on the same graph paper. Which car travels a greater distance after applying brakes?
Ans:
Convert speeds:
52 km/h = 14.44 m/s
3 km/h = 0.83 m/s
Distance travelled = area under speed–time graph For first car:
s1 = ½ × 5 × 14.44
= 36.1 m (approx.)
For second car:
s2 = ½ × 10 × 0.83
= 4.15 m (approx.)
So, the first car travels a greater distance after applying brakes.
Q6. The distance–time graph of three objects A, B, and C is shown in the figure. Study the graph and answer the following questions.
(a) Which of the three is the fastest?
(b) Do all three ever meet at the same point?
(c) When A overtakes B, how far has C travelled?
(d) When B overtakes C, how far has B travelled?
Ans:
(a) The fastest object is the one with the steepest slope in the graph. From the graph, B is the fastest.
(b) No, all three do not meet at the same point at the same time, because their graphs do not intersect at a single common point.
(c) A overtakes B at the point where their graphs intersect. From the graph, this happens at about 1 hour and around 8 km. At that time, C has travelled approximately 6 km.
(d) B overtakes C at their intersection point. From the graph, this occurs at about 0.5 hour and around 6 km. So, B has travelled approximately 6 km at that moment.
Q7. A ball is dropped gently from a height of 20 m. Its velocity increases uniformly at 10 m/s². With what velocity will it hit the ground? After how much time will it reach the ground?
Ans:
Given,
u = 0 (dropped gently)
a = 10 m/s²
s = 20 m
Using, v² = u² + 2as
v² = 0 + 2 × 10 × 20
v² = 400
v = 20 m/s
Time, v = u + at
20 = 0 + 10t
t = 2 s
So, the ball hits the ground with a velocity of 20 m/s after 2 seconds.
Q4. The speed–time graph of a car is shown in the figure.
(a) Find the distance travelled by the car in the first 4 seconds. Shade the region in the graph that represents this distance.
(b) Which part of the graph indicates uniform motion of the car?
Ans:
(a) Distance travelled in a speed–time graph = area under the graph.
From 0 to 4 seconds, the speed increases from 0 to about 6 m/s (approximately).
So, the area under the curve (approximate) can be taken as a triangle:
Distance ˜ ½ × base × height
= ½ × 4 × 6
= 12 m (approximately)
The shaded region should be the area under the curve from time 0 to 4seconds.
(b) The part of the graph where the line becomes horizontal (approximately from 6 s to 10 s) indicates uniform motion, because the speed remains constant in that interval.
Q9. Among the following situations, state which are possible and give one example of each.
(a) An object having constant acceleration but zero velocity.
(b) An object moving in a certain direction having acceleration perpendicular to its motion.
Ans:
(a) Possible.
Example: When a ball is thrown vertically upward, at its highest point, its velocity becomes zero. But at that moment, the acceleration is equal to the acceleration due to gravity (9.8 m/s²).
(b) Possible.
Example: When a car moves along a circular path, its acceleration acts perpendicular to the direction of motion.
Q10. An artificial satellite is moving in a circular orbit of radius 42,250km. If it completes one revolution around the Earth in 24 hours, find its speed.**
Ans:
Radius (r) = 42,250 km = 4.225 × 107m
Time (T) = 24 hours = 24 × 3600 = 86,400 s
Speed (v) = 2pi r/T
= 2 × 3.14 × 4.225 × 107/86400
= 2.6533 × 108/86400
≈ 3070 m/s
So, the speed of the satellite is approximately 3070 m/s.
Additional Questions & Answers
Q1. What is uniform motion?
Ans: When an object covers equal distances in equal intervals of time, it is called uniform motion.
Q2. What is non-uniform motion?
Ans: When an object covers unequal distances in equal intervals of time, it is called non-uniform motion.
Q3. Define speed. Write its SI unit.
Ans: Speed is the distance travelled by an object in unit time. Its SI unit ism/s.
Q4. What is velocity? What type of quantity is it?
Ans: Velocity is the speed of an object in a definite direction. It is a vector quantity.
Q5. Write the formula of average velocity.
Ans: Average velocity = Total displacement ÷ Total time
Q6. What is acceleration? Write its formula and SI unit.
Ans: Acceleration is the rate of change of velocity with time.
Formula: a = (v – u) / t
SI unit: m/s²
Q7. Define uniform and non-uniform acceleration. Give examples.
Ans: Uniform acceleration: When velocity changes by equal amounts in equal intervals of time.
Example: A freely falling stone.
Non-uniform acceleration: When velocity changes by unequal amounts in equal intervals of time.
Example: A car moving in traffic.
Q8. What is uniform circular motion?
Ans: When an object moves in a circular path with constant speed, it is called uniform circular motion.
Q9. Write the equations of motion.
Ans:
(a) v = u + at
(b) s = ut + ½at²
(c) v² – u² = 2as
Multiple Choice Questions (MCQ)
1. Which of the following is an example of uniform motion?
(a) A car moving with constant speed in a straight line
(b) A freely falling stone
(c) A car moving in a circle
(d) A swinging pendulum
Ans: (a)
2. The SI unit of speed is
(a) km/h
(b) m/s
(c) cm/s
(d) m/min
Ans: (b)
3. What does the slope of a distance-time graph represent?
(a) Acceleration
(b) Velocity
(c) Speed
(d) Displacement
Ans: (c)
4. Which of the following is a vector quantity?
(a) Speed
(b) Distance
(c) Velocity
(d) Time
Ans: (c)
5. A body is said to be in rest if
(a) it is not moving at all
(b) its position does not change with respect to time
(c) it moves slowly
(d) it has no energy
Ans: (b)
6. The distance covered by a body per unit time is called
(a) Velocity
(b) Acceleration
(c) Speed
(d) Displacement
Ans: (c)
7. Which of the following is not a scalar quantity?
(a) Distance
(b) Speed
(c) Velocity
(d) Time
Ans: (c)
8. The rate of change of velocity is called
(a) Speed
(b) Acceleration
(c) Distance
(d) Displacement
Ans: (b)
9. If a body moves with constant speed in a circular path, its motion is
(a) Uniform motion
(b) Non-uniform motion
(c) Rest
(d) Linear motion
Ans: (b)
10. What is the SI unit of acceleration?
(a) m/s
(b) m/s²
(c) km/h²
(d) cm/s
Ans: (b)
11. Which graph represents uniform motion?
(a) Straight line in distance-time graph
(b) Curved line in distance-time graph
(c) Horizontal line in velocity-time graph
(d) Vertical line in velocity-time graph
Ans: (a)
12. Displacement is
(a) always greater than distance
(b) always equal to distance
(c) shortest distance between initial and final positions
(d) always zero
Ans: (c)
13. When acceleration is zero, the motion is
(a) uniformly accelerated
(b) uniformly retarded
(c) uniform motion
(d) non-uniform motion
Ans: (c)
14. The change in velocity per unit time is called
(a) Speed
(b) Acceleration
(c) Distance
(d) Time
Ans: (b)
15. A body moving with constant velocity has
(a) zero acceleration
(b) increasing acceleration
(c) decreasing acceleration
(d) infinite acceleration
Ans: (a)
16. Which of the following is an example of non-uniform motion?
(a) A train moving at constant speed
(b) A car accelerating
(c) A person standing still
(d) A clock’s second hand
Ans: (b)
17. The area under a velocity-time graph gives
(a) Speed
(b) Acceleration
(c) Distance or displacement
(d) Time
Ans: (c)
18. If a body starts from rest, its initial velocity is
(a) zero
(b) one
(c) infinite
(d) negative
Ans: (a)
19. Retardation means
(a) increase in speed
(b) decrease in speed
(c) constant speed
(d) no motion
Ans: (b)
20. The SI unit of displacement is
(a) metre
(b) kilometre
(c) centimetre
(d) metre per second
Ans: (a)
21. Velocity is defined as
(a) distance covered per unit time
(b) displacement per unit time
(c) acceleration per unit time
(d) change in speed
Ans: (b)
22. Which of the following is true for uniform circular motion?
(a) Speed is constant
(b) Velocity is constant
(c) Acceleration is zero
(d) Displacement is zero
Ans: (a)
23. The slope of a velocity-time graph represents
(a) Speed
(b) Distance
(c) Acceleration
(d) Displacement
Ans: (c)
24. When a body moves equal distances in equal intervals of time, it has
(a) Non-uniform motion
(b) Uniform motion
(c) Acceleration
(d) Rest
Ans: (b)
25. Which quantity has both magnitude and direction?
(a) Speed
(b) Distance
(c) Velocity
(d) Time
Ans: (c)
26. A straight horizontal line on a velocity-time graph indicates
(a) increasing velocity
(b) decreasing velocity
(c) constant velocity
(d) zero velocity
Ans: (c)
27. If the velocity of a body increases uniformly, its motion is
(a) uniform
(b) uniformly accelerated
(c) non-uniform
(d) rest
Ans: (b)
28. The motion of a pendulum is
(a) uniform motion
(b) periodic motion
(c) rectilinear motion
(d) circular motion
Ans: (b)
29. Which of the following quantities can be zero?
(a) Speed
(b) Velocity
(c) Acceleration
(d) All of these
Ans: (d)
30. The total path covered by a body is called
(a) displacement
(b) speed
(c) distance
(d) velocity
Ans: (c)
