NCERT Physics Class 11 Chapter 2 Easy Line-by-Line Notes
Instantaneous Acceleration
“Instantaneous acceleration is defined in the same way as instantaneous velocity.”
• Just like instantaneous velocity gives velocity at one instant,
• Instantaneous acceleration gives acceleration at one instant.
Formula of Instantaneous Acceleration
• Take very small time interval.
• Find change in velocity.
• Divide by tiny time interval.
Calculus Form
“The acceleration at an instant is the slope of the tangent to the v–t curve.”
Important Graph Rule:
On velocity-time graph:
Slope of tangent = instantaneous acceleration
Velocity and Acceleration
“Velocity has both magnitude and direction.”
Velocity is a vector quantity.
It can change by:
- Changing speed
- Changing direction
- Changing both
“Acceleration may result from change in speed, direction or both.”
| Situation | Type of Change |
|---|---|
| Car speeding up | Speed changes |
| Circular motion | Direction changes |
| Curved fast motion | Both change |
Positive, Negative and Zero Acceleration
Positive Acceleration
- Velocity increases with time.
- Object speeds up.
Example: Bike accelerating forward.
Negative Acceleration (Retardation)
- Velocity decreases with time.
- Object slows down.
Example: Applying brakes.
Zero Acceleration
- Velocity remains constant.
- No change in motion.
Example: Car moving at constant speed.
Position-Time Graphs
“Graph curves upward for positive acceleration.”
• Slope keeps increasing.
• Object moves faster and faster.
“Graph curves downward for negative acceleration.”
• Slope decreases with time.
• Object slows down.
“Straight line for zero acceleration.”
• Constant slope.
• Constant velocity.
Constant Acceleration
“Our study will be restricted to constant acceleration.”
Acceleration remains same throughout motion.
Example: Free fall near Earth.
Equation for Constant Acceleration
Rearranging Equation
Meaning of Symbols
| Symbol | Meaning |
|---|---|
| v₀ | Initial velocity |
| v | Final velocity |
| a | Acceleration |
| t | Time |
Velocity-Time Graph Cases
Case (a)
Object moving in positive direction with positive acceleration.
- Velocity positive
- Acceleration positive
Object moves forward faster and faster.
Graph: Upward sloping line above time axis.
Case (b)
Object moving in positive direction with negative acceleration.
- Velocity positive
- Acceleration negative
Object still moves forward but slows down.
Example: Car braking while moving forward.
Case (c)
Object moving in negative direction with negative acceleration.
- Velocity negative
- Acceleration negative
Object moves backward and speeds up backward.
Case (d)
Object moving in positive direction till t₁ and then turns back.
- Initially moving forward
- Velocity becomes zero at t₁
- Then object reverses direction
Important Point: At turning point velocity becomes zero.
Area Under Velocity-Time Graph
“Area under the curve represents displacement.”
Very Important Concept
On velocity-time graph:
Why Area Gives Displacement
Constant Velocity Case
Velocity-time graph becomes:
- Straight horizontal line
Area rectangle under graph gives displacement.
Important Graph Rules Summary
| Graph | Slope Gives | Area Gives |
|---|---|---|
| Position-Time | Velocity | — |
| Velocity-Time | Acceleration | Displacement |
Real-Life Examples
| Situation | Acceleration Type |
|---|---|
| Bike speeding up | Positive |
| Car braking | Negative |
| Cruise control | Zero |
| Falling object | Constant acceleration |
Acceleration describes how velocity changes with time, and on a velocity-time graph, slope gives acceleration while area under the graph gives displacement.
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| Instantaneous acceleration on a velocity-time graph showing tangent slope and displacement area for Class 11 Physics students. |
CBSE Class 11 Physics Chapter 2 Important Questions and Answers – Instantaneous Acceleration
Very Short Answer Questions
What is instantaneous acceleration?
Instantaneous acceleration is the rate of change of velocity at a particular instant of time.
Write the formula for instantaneous acceleration.
a = lim (Δt → 0) (Δv / Δt)
What is the SI unit of acceleration?
The SI unit of acceleration is metre per second squared (m/s²).
Is acceleration a scalar or vector quantity?
Acceleration is a vector quantity because it has both magnitude and direction.
What does the slope of a velocity-time graph represent?
The slope of a velocity-time graph represents acceleration.
What does the area under a velocity-time graph represent?
The area under a velocity-time graph represents displacement.
Short Answer Questions
Define instantaneous acceleration.
Instantaneous acceleration is the acceleration of an object at a particular instant of time. Mathematically, it is expressed as:
a = dv/dt
It measures how quickly velocity changes at a given moment.
How can velocity change?
Velocity can change in three ways:
- Change in speed
- Change in direction
- Change in both speed and direction
Any of these changes produces acceleration.
Differentiate between positive and negative acceleration.
| Positive Acceleration | Negative Acceleration |
|---|---|
| Velocity increases with time. | Velocity decreases with time. |
| Object speeds up. | Object slows down. |
| Slope of v-t graph is positive. | Slope of v-t graph is negative. |
What is zero acceleration?
Zero acceleration occurs when velocity remains constant. There is no change in speed or direction.
Example: A car moving at constant speed on a straight road.
Long Answer Questions
Explain instantaneous acceleration using a velocity-time graph.
Instantaneous acceleration is the rate of change of velocity at a particular instant.
a = dv/dt
On a velocity-time graph, the instantaneous acceleration at any point is obtained by drawing a tangent at that point. The slope of the tangent gives the instantaneous acceleration.
Therefore:
Instantaneous Acceleration = Slope of Tangent to the v-t Graph
Explain positive, negative and zero acceleration with examples.
Positive Acceleration: Velocity increases with time. Example: A bike speeding up.
Negative Acceleration: Velocity decreases with time. Example: A car slowing down after brakes are applied.
Zero Acceleration: Velocity remains constant. Example: A train moving uniformly on a straight track.
Derive the first equation of motion.
For constant acceleration:
a = (v − v₀)/t
Multiplying both sides by t:
at = v − v₀
Rearranging:
v = v₀ + at
This is known as the first equation of motion.
Multiple Choice Questions (MCQs)
Instantaneous acceleration is represented by:
A. Δx/Δt
B. Δv/Δt
C. dv/dt
D. Both B and C
Answer: D. Both B and C
Area under a velocity-time graph gives:
A. Velocity
B. Acceleration
C. Displacement
D. Speed
Answer: C. Displacement
Slope of a velocity-time graph gives:
A. Velocity
B. Distance
C. Acceleration
D. Time
Answer: C. Acceleration
Assertion and Reason Questions
Assertion:
Acceleration can occur even when speed remains constant.
Reason:
Velocity changes when direction changes.
Answer: Both Assertion and Reason are true, and the Reason correctly explains the Assertion.
Assertion:
The area under a velocity-time graph gives displacement.
Reason:
Velocity is displacement per unit time.
Answer: Both Assertion and Reason are true, and the Reason correctly explains the Assertion.
Fill in the Blanks
Instantaneous acceleration is represented by dv/dt.
The slope of a velocity-time graph gives acceleration.
The area under a velocity-time graph gives displacement.
Negative acceleration is also called retardation.
At the turning point, velocity becomes zero.
Match the Following
| Column A | Column B |
|---|---|
| Slope of v-t graph | Acceleration |
| Area under v-t graph | Displacement |
| Constant velocity | Zero acceleration |
| Retardation | Negative acceleration |
Case Study Questions
A car starts moving with an initial velocity of 10 m/s and accelerates uniformly at 2 m/s² for 5 seconds.
What is the initial velocity of the car?
Answer: 10 m/s
What is the acceleration of the car?
Answer: 2 m/s²
Calculate the final velocity.
Using:
v = v₀ + at
v = 10 + (2 × 5) = 20 m/s
Answer: 20 m/s
Is the acceleration positive or negative?
Answer: Positive acceleration.
Which equation of motion is used?
Answer: v = v₀ + at
Definition
- Acceleration at a particular instant.
- Rate of change of velocity with time.
Formula
- Very small time interval considered.
- Change in velocity divided by time interval.
Velocity-Time Graph
- Slope of tangent gives acceleration.
- Positive slope → Positive acceleration.
- Negative slope → Negative acceleration.
Types of Acceleration
- Positive Acceleration
- Negative Acceleration (Retardation)
- Zero Acceleration
Velocity Changes By
- Changing Speed
- Changing Direction
- Changing Both
Position-Time Graph
- Upward Curve → Positive Acceleration
- Downward Curve → Negative Acceleration
- Straight Line → Zero Acceleration
Constant Acceleration
- Acceleration remains constant.
- Example: Free Fall.
Area Under v-t Graph
- Area under curve = Displacement
- Rectangle area for constant velocity.
Real-Life Examples
- Bike speeding up
- Car braking
- Cruise control
- Falling object
