Acceleration
│
├── Definition
│ ├── Rate of change of velocity
│ ├── Vector quantity
│ └── Has magnitude + direction
│
├── Velocity Change
│ ├── Change in speed
│ ├── Change in direction
│ └── Both speed and direction
│
├── Average Acceleration
│ ├── Formula
│ │ └── a = Δv / Δt
│ │
│ ├── Terms
│ │ ├── Δv = change in velocity
│ │ └── Δt = time interval
│ │
│ └── Direction
│ └── Same as Δv
│
├── Instantaneous Acceleration
│ ├── Acceleration at a particular instant
│ ├── Very small time interval
│ └── Formula
│ └── a = dv / dt
│
├── Motion in x-y Plane
│ ├── Velocity Components
│ │ ├── vx = v cosθ
│ │ └── vy = v sinθ
│ │
│ ├── Acceleration Components
│ │ ├── ax = dvx/dt
│ │ └── ay = dvy/dt
│ │
│ └── Vector Form
│ └── a = ax i + ay j
│
├── Graphical Understanding
│ ├── Velocity changes from point to point
│ ├── Δv found by vector subtraction
│ ├── Smaller Δt gives accurate acceleration
│ └── Δt → 0 gives instantaneous acceleration
│
├── Units
│ ├── SI Unit
│ │ └── m/s²
│ │
│ └── Dimensional Formula
│ └── [M⁰L¹T⁻²]
│
├── Special Cases
│ ├── Constant velocity
│ │ └── Acceleration = 0
│ │
│ ├── Negative acceleration
│ │ └── Retardation / Deceleration
│ │
│ └── Circular motion
│ └── Acceleration exists due to direction change
│
└── Important NEET Formulas
├── a = Δv / Δt
├── a = dv / dt
├── ax = dvx / dt
├── ay = dvy / dt
├── vx = v cosθ
└── vy = v sinθ
 |
| Class 11 Physics Acceleration Notes with Formulas and Vector Components for CBSE and NEET Students |
Acceleration Notes (NEET Level)
1. What is Acceleration?
Acceleration tells us how quickly velocity changes with time.
- If speed changes → acceleration exists.
- If direction changes → acceleration exists.
- If both change → acceleration exists.
Acceleration is a vector quantity because it has both magnitude and direction.
2. Average Acceleration
Average acceleration is defined as:
Where:
- a = average acceleration
- Δv = change in velocity
- Δt = time interval
3. Velocity Components in x-y Plane
In two-dimensional motion, velocity has two components:
- vx → velocity along x-axis
- vy → velocity along y-axis
Therefore acceleration becomes:
Where:
- i = unit vector along x-axis
- j = unit vector along y-axis
4. Components of Acceleration
Where:
- ax = acceleration along x-axis
- ay = acceleration along y-axis
5. Instantaneous Acceleration
Instantaneous acceleration means acceleration at a particular instant of time.
It is obtained when the time interval becomes extremely small.
6. Component Form of Instantaneous Acceleration
Meaning:
- ax = rate of change of velocity along x-axis
- ay = rate of change of velocity along y-axis
7. Graphical Understanding of Acceleration
Suppose an object moves from point P to another point after a small time interval Δt.
- The velocity changes from v to another value.
- The change in velocity is called Δv.
- The direction of acceleration is same as the direction of Δv.
As Δt becomes smaller:
- Average acceleration approaches instantaneous acceleration.
- The direction becomes more accurate.
8. Velocity Components
If velocity makes angle θ with x-axis:
Where:
- vx = horizontal component
- vy = vertical component
9. SI Unit of Acceleration
Read as: metre per second square
10. Dimensional Formula
11. Important NEET Points
- Acceleration depends on change in velocity.
- Constant velocity means acceleration is zero.
- Negative acceleration is called retardation or deceleration.
- In circular motion, acceleration exists even if speed is constant because direction changes continuously.
12. Formula Summary Table
| Concept | Formula |
|---|---|
| Average Acceleration | a = Δv / Δt |
| Instantaneous Acceleration | a = dv / dt |
| x-component | ax = dvx / dt |
| y-component | ay = dvy / dt |
| Velocity Components | vx = v cos θ, vy = v sin θ |
Quick Revision
- Acceleration = Rate of change of velocity.
- It is a vector quantity.
- SI unit = m/s².
- Velocity change can be due to speed or direction change.
- Average acceleration uses finite time interval.
- Instantaneous acceleration uses very small time interval.
Class 11 Physics - Acceleration Questions and Answers
1. Multiple Choice Questions (MCQs)
Q1. Acceleration is defined as:
A. Change in displacement
B. Change in speed
C. Change in velocity per unit time
D. Distance travelled per unit time
Answer: C. Change in velocity per unit time
Q2. SI unit of acceleration is:
A. m/s
B. m/s²
C. m²/s
D. km/h
Answer: B. m/s²
Q3. Which of the following is a vector quantity?
A. Distance
B. Speed
C. Time
D. Acceleration
Answer: D. Acceleration
2. Very Short Answer Questions
Q1. Define acceleration.
Answer: Acceleration is the rate of change of velocity with time.
Q2. Write the SI unit of acceleration.
Answer: m/s²
Q3. Is acceleration a scalar or vector quantity?
Answer: Vector quantity.
3. Short Answer Questions
Q1. Differentiate between average acceleration and instantaneous acceleration.
| Average Acceleration | Instantaneous Acceleration |
|---|---|
| Calculated over a finite time interval | Calculated at a particular instant |
| a = Δv / Δt | a = dv / dt |
| Gives average change | Gives exact change |
Q2. Why is acceleration a vector quantity?
Answer: Acceleration depends on change in velocity. Since velocity has both magnitude and direction, acceleration is also a vector quantity.
4. Long Answer Questions
Q1. Define average acceleration and derive its formula.
Average acceleration is the change in velocity divided by time interval.
If initial velocity = u
Final velocity = v
Time taken = Δt
Change in velocity:
Δv = v - u
Therefore,
a = Δv / Δt
Answer: Average acceleration is equal to change in velocity divided by time interval.
Q2. Explain instantaneous acceleration.
Instantaneous acceleration is acceleration at a particular instant of time. It is obtained when the time interval becomes extremely small.
a = dv / dt
Answer: Instantaneous acceleration gives exact acceleration at any instant.
5. Assertion and Reason Questions
Q1.
Assertion (A): Acceleration is a vector quantity.
Reason (R): Acceleration depends on change in velocity.
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true but R is not correct explanation
C. A is true but R is false
D. A is false but R is true
Answer: A
6. Fill in the Blanks
1. Acceleration is the rate of change of _______.
Answer: velocity
2. SI unit of acceleration is _______.
Answer: m/s²
3. Negative acceleration is called _______.
Answer: retardation
7. Case Study Questions
A car moves along a straight road. Its velocity changes from 10 m/s to 30 m/s in 5 seconds.
Q1. What is the change in velocity?
Answer: 20 m/s
Q2. Calculate acceleration.
a = (v - u)/t
a = (30 - 10)/5 = 4 m/s²
Answer: 4 m/s²
8. Statement Based Questions
Q1. Acceleration can exist without change in speed.
Answer: True
Q2. A body moving in circular path has acceleration.
Answer: True
Q3. Velocity and acceleration always act in same direction.
Answer: False
9. Match the Columns
| Column A | Column B |
|---|---|
| 1. Acceleration | a. m/s² |
| 2. Velocity | b. Vector quantity |
| 3. Retardation | c. Negative acceleration |
| 4. SI unit of acceleration | d. Rate of change of displacement |
Answers:
1 → b
2 → d
3 → c
4 → a
10. Important Formula Questions
Q1. Write formula for average acceleration.
a = Δv / Δt
Q2. Write formula for instantaneous acceleration.
a = dv / dt
Q3. Write acceleration components in x and y directions.
ax = dvx/dt
ay = dvy/dt
