I. Reflections on Concepts
Question 1
Distinguish between speed and velocity.
Answer:
|
Speed |
Velocity |
|
Speed is the distance travelled by an object per
unit time. |
Velocity is the displacement of an object per unit
time in a particular direction. |
|
It is a scalar quantity (only magnitude). |
It is a vector quantity (magnitude and
direction). |
|
Speed does not depend on direction. |
Velocity always includes direction. |
|
Example: A car moving at 60 km/h. |
Example: A car moving 60 km/h towards north. |
Explanation:
Speed only tells us how fast something is moving. Velocity tells us how
fast and in which direction it is moving. Therefore, two objects can have
the same speed but different velocities if their directions are different.
Question 2
Briefly explain about constant
acceleration.
Answer:
Constant acceleration means that the rate of change
of velocity remains the same during equal intervals of time.
Explanation:
If an object's velocity increases or decreases by the same amount every
second, the acceleration is constant.
Example:
If a car's velocity increases like this:
- 5
m/s at 1 s
- 10
m/s at 2 s
- 15
m/s at 3 s
The velocity increases by 5 m/s every second,
so the acceleration is constant.
Example in daily life:
A freely falling object under gravity experiences nearly constant
acceleration (9.8 m/s²).
Question 3
How can you say that a body is in motion
if no force is acting on it?
Answer:
According to Newton’s First Law of Motion, a body continues
in its state of rest or uniform motion unless an external force acts on it.
Explanation:
If a body is already moving with constant velocity, it will continue
moving without any external force acting on it.
Example:
- A
spacecraft moving in outer space keeps moving even after engines stop
because there is almost no friction.
Thus, a body can remain in motion without any force
acting on it, provided no force is needed to change its motion.
Question 4
Are average speed and average velocity
same? Explain why.
Answer:
No, average speed and average velocity are not
always the same.
Average Speed
Average Velocity
Explanation:
Distance and displacement are different.
Example:
If a person walks 100 m forward and then 100 m backward, then:
- Total
distance = 200 m
- Displacement
= 0
So,
- Average
speed ≠ 0
- Average
velocity = 0
Thus, they are generally different quantities.
Question 5
How do you measure instantaneous speed?
Answer:
Instantaneous speed is the speed of an object at a
particular moment of time.
Explanation:
It is measured using instruments that can record speed instantly.
Example instruments:
- Speedometer
in vehicles
- Radar
guns used by traffic police
Example:
If the speedometer of a car shows 60 km/h at a particular moment, that
is the instantaneous speed.
Question 6
Explain acceleration with an example.
Answer:
Acceleration is the rate of change of velocity with
time.
It can occur due to:
- change
in speed
- change
in direction
- or
both.
Example:
When a car starts from rest and increases its speed:
|
Time |
Velocity |
|
1 s |
5 m/s |
|
2 s |
10 m/s |
|
3 s |
15 m/s |
Here velocity is increasing every second.
Therefore, the car is accelerating.
Another example:
When a ball is thrown upward, gravity slows it down. This is negative
acceleration (deceleration).
II. Application of Concepts
Question 1
In the given figure distance–time graphs
showing motion of two cars A and B are given. Which car moves faster?
Answer:
Car A moves faster.
Explanation:
In a distance–time graph, the slope (steepness) represents speed.
- A
steeper line → greater speed
- A
less steep line → smaller speed
Since line A is steeper than B, car A covers
more distance in the same time, so it is faster.
Question 2
A train of length 50 m moves with a
constant speed of 10 m/s. Calculate the time taken by the train to cross a
bridge of length 250 m.
Answer:
Total distance to be covered:
Speed = 10 m/s
Time required = 30 seconds
Question 3
Draw the distance–time graph when the
speed of a body increases uniformly.
Answer:
When speed increases uniformly, the distance–time
graph is a curved line.
Explanation:
Since the body covers more distance every second, the graph bends upward
showing increasing speed.
Question 4
What is the average speed of a Cheetah
that sprints 100 m in 6 seconds?
Answer:
Average speed = 16.67 m/s
Question 5
Which is faster? A cheetah that sprints
100 m in 6 s or a rabbit that sprints 50 m in 2 s?
Answer:
Speed of cheetah:
Speed of rabbit:
Rabbit is faster
because 25 m/s > 16.67 m/s.
Question 6
A car travels at 80 km/h during the first
half hour and 40 km/h during the other half hour. Find the average speed.
Answer:
Since the time intervals are equal,
Average speed = 60 km/h
Question 7
A particle covers 10 m in the first 5 s
and 40 m in the next 5 s. Assume constant acceleration. Find initial speed,
acceleration and distance covered in next 1 s.
Answer:
Using equations of motion:
Results obtained are:
- Initial
velocity (u) = 7.66 m/s
- Acceleration
(a) = 13 m/s²
- Distance
in next 1 s = 8.33 m
These values are obtained using the motion equations:
III. Higher Order Thinking Questions
Question 1
When velocity is constant, can average
velocity over any time interval differ from instantaneous velocity?
Answer:
No, when velocity is constant, average velocity and
instantaneous velocity are the same.
Explanation:
- Instantaneous
velocity is velocity at a particular moment.
- Average
velocity is displacement divided by total
time.
If velocity does not change, the object moves with the
same velocity at every moment. Therefore, both values become equal.
Example:
If a car moves at 50 km/h continuously, then:
- Instantaneous
velocity = 50 km/h
- Average
velocity = 50 km/h
Question 2
The rabbit and tortoise race story. Draw
and explain the distance–time graph.
Answer:
In the story:
- The
rabbit runs very fast, then rests for some time.
- The
tortoise moves slowly but continuously without stopping.
Distance–time graph explanation:
1.
Rabbit's graph:
o Very
steep line (fast speed)
o Then
horizontal line (rest)
o Then
again steep line
2.
Tortoise's graph:
o Straight
line with constant slope (slow but steady speed)
Because the rabbit stopped for some time, the tortoise
continuously increased its distance and finally won the race.
Conclusion:
The story teaches that steady and continuous progress can be more effective
than fast but irregular effort.
Chapter 2: Motion
I. Reflections on Concepts
Question 1
Answer:
Speed and velocity are both quantities used to
describe how fast an object moves, but they are different in certain important
ways.
Speed is defined as the
distance travelled by an object per unit time. It tells us only how fast
the object is moving and does not include any information about direction.
Therefore, speed is called a scalar quantity, because it has only
magnitude.
Velocity, on the other
hand, is defined as the displacement of an object per unit time in a
specific direction. Since it includes both magnitude and direction,
velocity is called a vector quantity.
Key Differences:
|
Speed |
Velocity |
|
Distance travelled per unit time |
Displacement per unit time |
|
Scalar quantity (only magnitude) |
Vector quantity (magnitude and direction) |
|
Direction is not considered |
Direction is important |
|
Always positive |
Can be positive, negative or zero |
Thus, speed tells how fast an object moves,
while velocity tells how fast and in which direction it moves.
Question 2
Answer:
Acceleration is defined as the rate of change of
velocity with respect to time.
When the change in velocity is the same during
equal intervals of time, the acceleration is called constant
acceleration or uniform acceleration.
This means that the velocity of an object increases or
decreases by the same amount every second.
Example:
Consider a car that increases its speed as follows:
|
Time (seconds) |
Velocity (m/s) |
|
1 |
5 |
|
2 |
10 |
|
3 |
15 |
|
4 |
20 |
Here the velocity increases by 5 m/s every second,
which means the acceleration is constant.
Thus, constant acceleration occurs when velocity
changes uniformly over time.
Question 3
Answer:
A body is said to be in motion if its position
changes with respect to time and with respect to a reference point.
If the position of an object keeps changing compared
to its surroundings, we say that the object is moving.
Example:
- A
car moving on a road changes its position with respect to trees,
buildings, and signboards.
- Therefore,
the car is said to be in motion.
However, motion is not an absolute property; it
is a relative property.
This means that whether an object is in motion or at
rest depends on the observer or reference point.
Example:
A person sitting in a moving bus:
- With
respect to other passengers in the bus → the person is at rest.
- With
respect to people standing on the road → the person is in motion.
Thus, motion depends on the frame of reference,
and it is not a common property that is the same for all observers.
Question 4
Answer:
Average speed and average velocity are not always
the same, because they are calculated using different physical quantities.
Average Speed
Average speed is the total distance travelled
divided by the total time taken.
Average Velocity
Average velocity is the total displacement divided
by the total time taken.
The difference arises because distance and
displacement are different.
- Distance
is the total path travelled.
- Displacement
is the shortest distance between the initial and final positions in a
particular direction.
Example:
Suppose a person walks 100 m forward and then
returns 100 m back to the starting point.
Therefore,
This example shows that average speed and average
velocity are generally different, except when motion is in a straight line
without changing direction.
Question 5
Answer:
Instantaneous speed is the speed of an object at a
particular moment of time.
It is different from average speed because it
represents the exact speed at a specific instant, rather than over a
time interval.
Instantaneous speed is commonly measured using special
instruments that can record speed instantly.
The most common instrument used to measure
instantaneous speed is a speedometer, which is found in vehicles such as
cars, buses, and motorcycles.
Example:
If the speedometer of a car shows 60 km/h at a
particular moment, it means the instantaneous speed of the car at that
moment is 60 km/h.
Traffic police also use radar speed guns to
measure the instantaneous speed of vehicles on highways.
Thus, instantaneous speed helps us know how fast an
object is moving at a specific instant of time.
Question 6
Answer:
Acceleration is defined as the rate at which the
velocity of an object changes with time.
An object is said to be accelerating if:
- its
speed increases,
- its
speed decreases, or
- its
direction changes.
Acceleration can therefore occur even if the speed
remains the same but the direction changes.
Mathematically,
Example 1: Increasing Speed
When a car starts from rest and gradually increases
its speed, it is accelerating.
For example:
|
Time (s) |
Velocity (m/s) |
|
1 |
2 |
|
2 |
4 |
|
3 |
6 |
The velocity increases every second, which shows that
the car is accelerating.
Example 2: Decreasing Speed
When a moving car applies brakes, its speed decreases.
This is called negative acceleration or deceleration.
Example 3: Change in Direction
When a car moves around a circular track, its
direction continuously changes. Even if its speed remains constant, it still
experiences acceleration.
Thus, acceleration describes how quickly the
velocity of an object changes.
II. Application of Concepts
Question 1
- If
the graph is steeper, the object is moving faster.
- If
the graph is less steep, the object is moving slower.
In the given graph, the line representing Car A is
steeper than the line for Car B. This means that in the same amount of
time, Car A covers more distance than Car B.
Therefore, Car A has greater speed and moves faster.
Question 2
Answer:
When a train crosses a bridge, it must travel a
distance equal to:
Total Distance = Length of Train + Length
of Bridge
Speed of the train = 10 m/s
Time taken is calculated using the formula:
Question 3
- The
object covers more distance in each successive second.
- The
speed continuously increases.
Because of this increase in speed, the graph does
not remain straight. Instead, it becomes a curve that gets steeper with
time.
Thus, the distance–time graph for increasing speed is a
rising curved line.
Question 4
Answer:
Average speed is calculated using:
Question 5
Answer:
First calculate their speeds.
Speed of Cheetah
Speed of Rabbit
Comparison:
25 m/s > 16.67 m/s
Question 6
Answer:
First calculate the distance travelled.
Distance in First Half Hour
Distance = Speed × Time
Distance = 40 × 0.5 = 20 km
Distance in Second Half Hour
Distance = 80 × 0.5 = 40 km
Total Distance
20 + 40 = 60 km
Total Time
0.5 + 0.5 = 1 hour
Average Speed
Question 7
1.
Initial speed
2.
Acceleration
3.
Distance covered in the next 5 seconds
Answer:
Using the equation of motion:
After solving the equations obtained from the two
intervals:
- Initial
velocity (u) = 1 m/s
- Acceleration
(a) = 0.8 m/s²
Distance covered in the next 5 seconds (from 10
s to 15 s):
Using motion equations,
Distance = 60 m
Final Answers:
III. Higher Order Thinking Questions
Question 1
Explanation:
- Instantaneous
velocity is the velocity at a specific
moment.
- Average
velocity is the total displacement divided by
total time.
If velocity remains constant:
- The
object moves with the same speed and direction at every moment.
- Therefore,
the velocity at any instant is the same as the average velocity.
Thus, they are equal when motion is uniform.
Question 2
Answer:
Explanation of the Distance–Time Graph:
1.
Rabbit's motion
o Initially
the rabbit runs very fast, so the graph is steep.
o Then
the rabbit stops to rest, so the graph becomes horizontal
(distance does not change).
o Later
the rabbit runs again towards the finish line.
2.
Tortoise's motion
o The
tortoise moves slowly but steadily.
o Its
graph is a straight line with a small slope.
Because the tortoise keeps moving continuously without
stopping, it eventually reaches the finish line while the rabbit wastes time
resting.
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