- (a) velocity of the moving object
- (b) displacement covered by the moving object
- (c) speed of the moving object
- (d) acceleration of the moving object
Answer:
(b) displacement covered by the moving object
- (a) Motion of the Earth around the Sun
- (b) Motion of a toy train on a circular track
- (c) Motion of a racing car on a circular track
- (d) Motion of the hour hand on a clock dial
Answer:
(c) Motion of a racing car on a circular track
- (a) a real force
- (b) the reaction force of centripetal force
- (c) a virtual force
- (d) directed towards the centre of the circular path
Answer:
(c) a virtual force
- Speed is a scalar quantity whereas velocity is a vector quantity.
- The slope of the distance-time graph at any point gives speed.
- Negative acceleration is called retardation or deceleration.
- Area under the velocity-time graph shows displacement.
If false, correct the statement.
Answer: False. The statement is incorrect. The motion of a city bus in heavy traffic is an example of non-uniform motion, not uniform motion. In heavy traffic, a bus constantly changes its speed and direction as it accelerates, decelerates, and turns to navigate through congested roads. Uniform motion occurs when an object travels equal distances in equal intervals of time at a constant velocity. Since a city bus in heavy traffic does not maintain constant velocity, its motion is non-uniform. Examples of uniform motion would include a car traveling at a constant speed on a straight highway or a train moving at a steady speed on a straight track.
Answer: True. Acceleration can indeed have a negative value. Negative acceleration, also called deceleration or retardation, occurs when an object's velocity decreases over time. For example, when a moving car applies brakes, its velocity decreases in the direction of motion, resulting in negative acceleration. Mathematically, if the change in velocity is negative, the acceleration will be negative. Negative acceleration does not mean the object is moving backward; it simply indicates that the velocity is decreasing in the chosen positive direction.
Answer: True. Distance covered by a particle never becomes zero but displacement can become zero. Distance is the total path length traveled by an object and is always positive or zero, never negative. Even if an object returns to its starting point, the distance traveled remains the sum of all path segments. However, displacement is the shortest straight-line distance between the initial and final positions, including direction. When an object returns to its starting point, the final position coincides with the initial position, making the displacement zero even though the distance traveled is not zero. For example, if a person walks 5 km away from home and then walks 5 km back home, the distance is 10 km but displacement is zero.
Answer: False
Correct Statement:
The velocity-time graph of a freely falling body is a straight line inclined to the x-axis because velocity increases uniformly with time.
Answer: False
Correct Statement:
If the velocity-time graph is a straight inclined line, the displacement-time graph will be a curve because the body is uniformly accelerated.
Correction made:
Original answer marked as True was incorrect.
Choose the correct option:
- (a) Both assertion and reason are true and reason is the correct explanation.
- (b) Both assertion and reason are true but reason is not the correct explanation.
- (c) Assertion is true but reason is false.
- (d) Assertion is false but reason is true.
Answer: (c) Assertion is true but reason is false. The assertion is correct because accelerated motion can result from a change in the magnitude of velocity, a change in the direction of velocity, or changes in both magnitude and direction simultaneously. The reason is false because acceleration can be produced not only by a change in magnitude of velocity but also by a change in direction of velocity while the magnitude remains constant. For instance, in uniform circular motion, the speed remains constant but the direction continuously changes, producing centripetal acceleration. Therefore, the assertion accurately describes the nature of acceleration, but the reason provides an incomplete explanation.
Answer: (d) Assertion is false but reason is true. The assertion is incorrect because a speedometer of a car measures instantaneous speed, which is the speed at a particular instant of time, not the average speed over the entire journey. Average speed is calculated as total distance divided by total time taken. The reason is true because average velocity is correctly defined as total displacement divided by total time taken. This is an important distinction: while a speedometer gives the speed at any given moment, average speed requires knowledge of the entire path traveled over the complete time interval.
Answer: (a) Both assertion and reason are true and reason is the correct explanation. The assertion is true because displacement of a body can be zero when distance travelled is not zero. This occurs when an object returns to its starting point after traveling along a path. For example, if a person walks 10 meters north and then 10 meters south, returning to the original position, the total distance traveled is 20 meters but the displacement is zero. The reason correctly explains why this is possible: displacement is defined as the shortest distance between initial and final positions along with direction, whereas distance is the total length of the path actually traveled. Since displacement depends only on the initial and final positions and not on the path taken, it can be zero even when the distance traveled is substantial. The reason directly explains the assertion, making it the correct explanation for why displacement can be zero while distance is not.
| List I | List II |
|---|---|
| Motion covering equal distances in equal intervals of time | Uniform motion |
| Motion with non-uniform acceleration | Non-uniform motion |
| Constant retardation | Negative acceleration |
| Uniform acceleration | Constant acceleration |
The original uploaded content was incomplete. The matching was logically completed based on standard textbook concepts.
Answer:
Velocity is the rate of change of displacement with respect to time.
- Velocity is a vector quantity.
- SI unit of velocity is (m/s).
| Distance | Displacement |
|---|---|
| Actual length of path travelled | Shortest distance between initial and final position |
| Scalar quantity | Vector quantity |
| Non-negative; it can be zero | Can be positive, negative, or zero |
| Depends on path | Independent of path |
Answer: An object is said to be in uniform motion if it covers equal distances in equal intervals of time. This means the object travels the same distance in every equal time period, regardless of how small or large that time interval is. In uniform motion, the velocity of the object remains constant, both in magnitude and direction. The object does not speed up, slow down, or change direction. Examples of uniform motion include a car traveling at a constant speed of 60 km/h on a straight road, or a train moving at constant velocity on a straight track. Uniform motion is characterized by zero acceleration since there is no change in velocity.
| Speed | Velocity |
|---|---|
| Rate of change of distance | Rate of change of displacement |
| Scalar quantity | Vector quantity |
| Magnitude only | Magnitude and direction |
| Non-negative; it can be zero | Can be positive, negative, or zero |
| SI unit: m/s | SI unit: m/s |
Answer:
When velocity decreases with time, acceleration becomes negative.
Negative acceleration is called:
- Retardation
- Deceleration
Answer: Yes, uniform circular motion is accelerated. In uniform circular motion, an object moves in a circular path at constant speed. Although the magnitude of velocity remains constant, the direction of velocity continuously changes at every point along the circular path. Since acceleration is defined as the rate of change of velocity, and velocity includes both magnitude and direction, a change in direction constitutes a change in velocity. Therefore, even though the speed is uniform, the motion is accelerated. This acceleration is directed toward the center of the circle and is called centripetal acceleration. It is responsible for continuously changing the direction of the object's motion to keep it moving in a circular path.
Answer:
When an object moves with constant speed along a circular path, the motion is called uniform circular motion.
Examples:
- Earth revolving around the Sun
- Moon revolving around the Earth
First Equation of Motion
From velocity-time graph:
Rearranging,
This is the first equation of motion.
Second Equation of Motion
Displacement is equal to area under velocity-time graph.
This is the second equation of motion.
Third Equation of Motion
Using:
Substituting into:
We get:
This is the third equation of motion.
(i) Linear Motion
Motion along a straight line.
Example:
- Car moving on a straight road
(ii) Circular Motion
Motion along a circular path.
Example:
- A point on the rim of a rotating wheel
(iii) Oscillatory Motion
To-and-fro motion repeated at regular intervals.
Example:
- Pendulum of a clock
(iv) Rotational Motion
Motion of a body about its own axis.
Example:
- Rotation of a spinning top
(v) Random Motion
Irregular and unpredictable motion.
Example:
- Brownian motion of dust particles in air
Given:
(a) Final Velocity
Using:
(b) Time Taken
Using:
Answer:
- Final velocity = (20m/s)
- Time taken = (2s)
Given:
- Diameter = 200 m
- Radius = 100 m
- Time for one round = 40 s
- Total time = 2 min 20 s = 140 s
Speed
Distance Covered
Displacement
Number of rotations:
After 3.5 rotations, athlete reaches opposite side of circle.
Displacement = diameter = (200m)
Given:
Using:
Answer:
Distance covered = (200m)
Fixed and Movable Objects
Immovable Objects:
- Houses
- Trees
- Plants
Movable Objects:
- Birds
- Cars
- Buses
Observation:
- Bus in heavy traffic covers unequal distances in equal intervals of time.
- Train in uniform motion covers equal distances in equal intervals of time.
Conclusion:
- Bus → Non-uniform motion
- Train → Uniform motion
Observation:
- Distance through path ABC:
- Distance AC:
- Shortest path from A to D:
- Total distance in path ABCDA:
Observation:
- Stone and eraser reach ground almost together.
- Eraser falls faster than paper.
- Crumpled paper falls faster than plain paper.
Reason:
Air resistance depends on surface area exposed to air. Larger surface area experiences greater air resistance.
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