Acceleration
Defines average and instantaneous acceleration and its relation to velocity change.
What is Acceleration?
The rate of change of velocity of an object with respect to time. It is a vector quantity.
Key formula / rule: Average Acceleration
Key points
- Define average and instantaneous acceleration.
- Distinguish between positive, negative, and zero acceleration.
- Calculate average acceleration from given velocity and time data.
- Determine instantaneous acceleration from a velocity-time function using differentiation.
Common exam trap
Confusing acceleration with speed or velocity.
Definitions
- Term
Acceleration
- Meaning
The rate of change of velocity of an object with respect to time. It is a vector quantity.
- Term
Average Acceleration
- Meaning
The total change in velocity divided by the total time taken for that change.
- Term
Instantaneous Acceleration
- Meaning
The acceleration of an object at a particular instant in time, given by the derivative of velocity with respect to time.
- Term
Deceleration (Retardation)
- Meaning
A term used when the acceleration is in the direction opposite to the velocity, causing the object to slow down.
Learning objectives
Define average and instantaneous acceleration.
Distinguish between positive, negative, and zero acceleration.
Calculate average acceleration from given velocity and time data.
Determine instantaneous acceleration from a velocity-time function using differentiation.
Interpret acceleration from position-time and velocity-time graphs.
Relate acceleration to the change in velocity and direction of motion.
Formulae
- Name
Average Acceleration
- Note
Represents the overall rate of change of velocity over a time interval Δt.
- Expression
aavg = (vf - vi) / (tf - ti) = Δv / Δt
- Name
Instantaneous Acceleration
- Note
The acceleration at a specific instant, found by differentiating the velocity function with respect to time.
- Expression
a = dv/dt
- Name
Instantaneous Acceleration (from position)
- Note
The second derivative of the position function with respect to time.
- Expression
a = d²x/dt²
Prerequisites
Basic understanding of displacement, distance, speed, and velocity.
Concept of scalars and vectors.
Basic differentiation (for instantaneous acceleration).
Understanding of graphs (position-time, velocity-time).
Common mistakes
Confusing acceleration with speed or velocity.
Assuming negative acceleration always means slowing down (it can mean speeding up in the negative direction).
Not considering the vector nature of acceleration and velocity.
Incorrectly applying kinematic equations when acceleration is not constant.
Mistaking instantaneous acceleration for average acceleration.
Units errors (e.g., using m/s instead of m/s²).
Keywords
Acceleration
Velocity
Rate of change
Vector
Average acceleration
Instantaneous acceleration
Differentiation
Kinematics
Uniform acceleration
Non-uniform acceleration
Deceleration
Retardation
Practice preview
If a car's velocity changes from 10 m/s to 20 m/s in 5 seconds, what is its average acceleration?…
easy
A car accelerates from rest at a rate of 5 m/s². What is its velocity after 4 seconds?…
medium
Which of the following statements about acceleration is correct?…
easy