Class 11 Physics Chapter 2: Motion in a Straight Line – Notes & Questions
Class 11 Physics Chapter 2: Motion in a Straight Line
Class 11 Physics Chapter 2 – Motion in a Straight Line is the chapter where the language of motion begins to make sense. Before worrying about complicated mechanics, we first learn how to describe where an object is, how fast it is moving and whether its motion is changing.
These notes are written in a simple, student-friendly way for CBSE Class 11 Physics. The aim is not just to memorise formulas, but to understand what each quantity actually tells us.
1. What is Motion?
An object is said to be in motion when its position changes with time relative to a chosen reference point or frame of reference.
For example, a student sitting inside a moving bus is at rest relative to another passenger, but is moving relative to a person standing on the road. So, motion is not absolute; it depends on the reference frame we choose.
2. Frame of Reference
A frame of reference is a reference system with respect to which we describe the position and motion of an object.
In simple one-dimensional motion, we normally choose a straight coordinate axis, such as the x-axis, and specify a positive direction.
3. Position and Position Coordinate
The position of an object tells us where the object is located relative to the chosen origin.
For motion along the x-axis, the position can be represented by the coordinate x.
If an object moves from position x1 to position x2, its change in position is called displacement.
4. Distance and Displacement
Distance
Distance is the total length of the actual path travelled by an object.
- It is a scalar quantity.
- It has magnitude only.
- It is always zero or positive.
- SI unit: metre (m).
Displacement
Displacement is the change in position of an object. In one-dimensional motion:
Δx = x2 − x1
- It is a vector quantity.
- It has magnitude and direction.
- It may be positive, negative or zero.
- Its magnitude can never be greater than the distance travelled.
Distance asks, “How much ground did you cover?”
Displacement asks, “How far and in which direction are you from where you started?”
Example
Suppose a student walks 5 m east and then 2 m west.
Distance = 5 + 2 = 7 m
Taking east as positive: Displacement = 5 − 2 = 3 m east
5. Speed and Velocity
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 interval.
| Quantity | Based on | Type | SI Unit |
|---|---|---|---|
| Average speed | Distance | Scalar | m/s |
| Average velocity | Displacement | Vector | m/s |
Important Relation
The magnitude of average velocity is always less than or equal to average speed.
They become equal when the object moves in a straight line without changing its direction.
6. Instantaneous Velocity and Speed
Average velocity tells us about motion over a time interval. But sometimes we want to know the velocity at one particular instant, just like the speed shown by a vehicle's speedometer.
This is called instantaneous velocity.
In simple words, instantaneous velocity is the rate of change of position with respect to time.
The magnitude of instantaneous velocity gives instantaneous speed.
7. Acceleration
Acceleration tells us how quickly velocity changes with time.
Instantaneous acceleration is written as:
The SI unit of acceleration is m/s².
Positive and Negative Acceleration
The sign of acceleration depends on the chosen positive direction. Negative acceleration is often called retardation or deceleration, but students should remember that a negative acceleration does not automatically mean that the object is slowing down. Whether an object speeds up or slows down depends on the relative signs of velocity and acceleration.
8. Graphs of Motion
Graphs are extremely important in this chapter. They allow us to understand motion visually instead of depending only on equations.
Position-Time Graph
The slope of a position-time graph gives velocity.
- Straight line with constant positive slope → constant positive velocity.
- Horizontal line → object is at rest.
- Negative slope → negative velocity.
- Changing slope → changing velocity.
Velocity-Time Graph
The slope of a velocity-time graph gives acceleration.
The area under a velocity-time graph represents displacement.
Acceleration-Time Graph
The area under an acceleration-time graph gives the change in velocity.
9. Equations of Uniformly Accelerated Motion
When acceleration remains constant, the following three equations are especially useful.
Here:
- u = initial velocity
- v = final velocity
- a = constant acceleration
- t = time
- s = displacement
Another Useful Relation
This relation follows from the fact that, for constant acceleration, average velocity is:
10. Motion Under Gravity: Free Fall
When an object falls under the influence of Earth's gravitational force, ignoring air resistance, it is said to be in free fall.
The acceleration due to gravity is represented by g. Near Earth's surface, its approximate value is:
Depending on the chosen positive direction, the sign of g may be positive or negative. The important thing is to use a consistent sign convention throughout the solution.
11. Common Mistakes Students Make
- Confusing distance with displacement.
- Using distance instead of displacement in average velocity.
- Forgetting the sign of velocity or acceleration.
- Using equations of uniformly accelerated motion when acceleration is not constant.
- Reading the area of a v-t graph as distance without considering direction.
- Forgetting to convert km/h into m/s in numerical problems.
- Changing the positive direction halfway through a problem.
12. One-Minute Revision
| Concept | Remember |
|---|---|
| Distance | Total path length; scalar. |
| Displacement | Change in position; vector. |
| Speed | Rate of change of distance. |
| Velocity | Rate of change of displacement. |
| Acceleration | Rate of change of velocity. |
| x-t graph slope | Velocity. |
| v-t graph slope | Acceleration. |
| v-t graph area | Displacement. |
| a-t graph area | Change in velocity. |
Class 11 Physics Chapter 2 Important Questions
The following questions are useful for school tests, periodic tests, annual examinations and concept revision. Try solving them yourself before opening the answer.
Very Short Answer Questions
- What is meant by a frame of reference?
- Define displacement.
- Is distance a scalar or vector quantity?
- Is displacement always smaller than distance?
- Define average velocity.
- What is instantaneous velocity?
- What is the SI unit of acceleration?
- What does the slope of a position-time graph represent?
- What does the slope of a velocity-time graph represent?
- What does the area under a velocity-time graph represent?
Short Answer Questions
- Explain why motion is said to be relative.
- Distinguish between distance and displacement.
- Differentiate between speed and velocity.
- Explain average velocity and instantaneous velocity.
- What is uniform motion? Give one example.
- What is non-uniform motion?
- Explain the physical meaning of acceleration.
- Why can displacement be zero even when distance travelled is not zero?
- Explain the significance of the slope of an x-t graph.
- Explain how displacement can be obtained from a velocity-time graph.
Conceptual Questions with Answers
Answer: Yes. If an object returns to its starting point, its displacement becomes zero, but the distance travelled is the total length of the path and is non-zero.
Answer: No. The magnitude of displacement is always less than or equal to the distance travelled.
Answer: Yes. Velocity depends on both magnitude and direction. If the direction changes while speed remains constant, velocity changes.
Answer: Yes. At an instant when an object's velocity becomes zero, its acceleration can still be non-zero. A familiar example is a ball at the highest point of its upward motion.
Answer: No. Negative acceleration simply means that acceleration is directed opposite to the chosen positive direction. The object slows down only when velocity and acceleration have opposite signs.
Important Numerical Problems
Numerical 1: Average Speed
A car travels a distance of 120 m in 10 s. Find its average speed.
Solution:
= 120 / 10
= 12 m/s
Answer: 12 m/s
Numerical 2: Average Velocity
A particle moves from x = 2 m to x = 17 m in 5 s. Find its average velocity.
Solution:
Answer: 3 m/s
Numerical 3: Using v = u + at
A car starts with an initial velocity of 5 m/s and accelerates uniformly at 2 m/s² for 6 s. Find its final velocity.
Given:
- u = 5 m/s
- a = 2 m/s²
- t = 6 s
v = 5 + (2 × 6)
v = 17 m/s
Answer: 17 m/s
Numerical 4: Finding Displacement
A body starts with velocity 4 m/s and moves with constant acceleration of 3 m/s² for 5 s. Find its displacement.
Solution:
s = 20 + 37.5
s = 57.5 m
Answer: 57.5 m
Numerical 5: Finding Acceleration
The velocity of a particle changes from 10 m/s to 25 m/s in 5 s. Find its average acceleration.
a = (25 − 10) / 5
a = 3 m/s²
Answer: 3 m/s²
Numerical 6: Using v² = u² + 2as
A particle moving at 10 m/s accelerates uniformly at 2 m/s². Find its velocity after travelling 75 m.
Given:
- u = 10 m/s
- a = 2 m/s²
- s = 75 m
v² = 10² + 2(2)(75)
v² = 100 + 300
v² = 400
v = 20 m/s
Answer: 20 m/s
Numerical 7: Object Coming to Rest
A car moving at 20 m/s comes to rest uniformly in 5 s. Find its acceleration.
a = (0 − 20) / 5
a = −4 m/s²
The negative sign indicates that acceleration is opposite to the chosen direction of motion.
Answer: −4 m/s²
Assertion-Reason Practice
1. Assertion: Displacement can be zero even when distance is not zero.
Reason: Displacement depends only on initial and final positions.
Answer: Both statements are true, and the reason correctly explains the assertion.
2. Assertion: Average speed is always greater than average velocity.
Reason: Speed is a scalar and velocity is a vector.
Answer: The assertion as written is not always correct. The correct relation is: |average velocity| ≤ average speed.
Multiple Choice Questions
-
Which quantity is a vector?
A. Distance B. Speed C. Displacement D. Time
Answer: C. Displacement -
The slope of a velocity-time graph represents:
A. Distance B. Acceleration C. Displacement D. Speed
Answer: B. Acceleration -
The area under a velocity-time graph gives:
A. Acceleration B. Speed C. Displacement D. Force
Answer: C. Displacement -
The SI unit of acceleration is:
A. m/s B. m/s² C. km/h D. N
Answer: B. m/s² -
If an object returns to its initial position, its displacement is:
A. Maximum B. Equal to distance C. Zero D. Negative
Answer: C. Zero -
Which equation does not contain time explicitly?
A. v = u + at
B. s = ut + ½at²
C. v² = u² + 2as
D. s = [(u + v)/2]t
Answer: C. v² = u² + 2as
Class 11 Physics Chapter 2 FAQs
1. What is Chapter 2 of Class 11 Physics?
In the current CBSE/NCERT Class 11 Physics sequence, Chapter 2 is Motion in a Straight Line.
2. Is Motion in a Straight Line important for CBSE Class 11 Physics?
Yes. It is one of the foundation chapters of mechanics. Concepts such as displacement, velocity, acceleration and motion graphs are used repeatedly in later chapters.
3. What are the most important formulas in Motion in a Straight Line?
The key equations for uniformly accelerated motion are:
4. What is the difference between distance and displacement?
Distance is the total path length travelled by an object, whereas displacement is the change in its position. Distance is scalar, while displacement is vector.
5. What is the difference between speed and velocity?
Speed is the rate of change of distance and has no direction. Velocity is the rate of change of displacement and has direction.
6. Can displacement be negative?
Yes. In one-dimensional motion, displacement can be positive, negative or zero depending on the chosen positive direction.
7. Can distance be negative?
No. Distance represents the total length of the path and is always non-negative.
8. What does the slope of an x-t graph represent?
The slope of a position-time graph represents velocity.
9. What does the slope of a v-t graph represent?
The slope of a velocity-time graph represents acceleration.
10. What does the area under a v-t graph represent?
The area under a velocity-time graph represents displacement.
11. What is instantaneous velocity?
Instantaneous velocity is the velocity of an object at a particular instant. Mathematically, it is the rate of change of position with respect to time:
12. What is acceleration?
Acceleration is the rate of change of velocity with time. Its SI unit is m/s².
13. When can average speed and the magnitude of average velocity be equal?
They can be equal when the object travels along a straight path without reversing its direction.
14. What is free fall?
Free fall is motion under the influence of gravity alone, when effects such as air resistance are neglected.
How to Prepare Chapter 2 for an Exam
- First understand the five basic words: distance, displacement, speed, velocity and acceleration.
- Practise graphs: Learn what slope and area mean, rather than memorising them mechanically.
- Memorise the three equations only after understanding them.
- Solve sign-convention questions. These are a common source of mistakes.
- Practise numericals without looking at the solution.
- Revise units. A correct calculation with an incorrect unit is still an incomplete physics answer.
Quick Formula Sheet
| Quantity / Relation | Formula |
|---|---|
| Displacement | Δx = x2 − x1 |
| Average speed | Total distance / Total time |
| Average velocity | Total displacement / Total time |
| Instantaneous velocity | v = dx/dt |
| Average acceleration | a = (v − u)/t |
| Instantaneous acceleration | a = dv/dt |
| First equation | v = u + at |
| Second equation | s = ut + ½at² |
| Third equation | v² = u² + 2as |
| Average velocity for constant acceleration | (u + v)/2 |
Final Revision Checklist
- What is a frame of reference?
- What is the difference between distance and displacement?
- What is the difference between speed and velocity?
- What is instantaneous velocity?
- What is acceleration?
- What does the slope of an x-t graph mean?
- What does the slope of a v-t graph mean?
- What does the area under a v-t graph mean?
- Can displacement be zero while distance is non-zero?
- Can velocity be zero while acceleration is non-zero?
- Can negative acceleration mean increasing speed?
- Can you use all three equations of motion confidently?
Conclusion
Motion in a Straight Line may look like a formula-heavy chapter at first, but the ideas are actually connected. Position leads to displacement, displacement leads to velocity, and velocity leads to acceleration. Once this chain is clear, the equations and graphs become much easier to understand.
For the best preparation, read these notes along with your NCERT textbook and then practise numerical problems. Physics becomes much easier when you stop treating every formula as a separate fact and start seeing how the quantities are related.
Study smart, practise regularly, and always write the units.
Note: These study notes are independently written for learning and revision. Students should refer to the latest CBSE syllabus and NCERT textbook for the prescribed course content.
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