3aAcceleration
Understand how velocity changes over time, calculate acceleration using a = (v_f − v_i) / t, and distinguish positive, negative, and zero acceleration.
Acceleration is the bridge between kinematics and dynamics. Every time you feel pushed back in a seat or feel your stomach drop, you are experiencing acceleration — mastering it unlocks all of Newton's laws.
Lesson Overview
Acceleration describes how quickly velocity changes over time. In this lesson you will learn the definition of acceleration, its formula and units, the difference between positive and negative acceleration, deceleration, and the distinction between average and instantaneous acceleration.
Key Concepts
Definition
Acceleration = rate of change of velocity: a = (v_f − v_i) / t
Units
Meters per second squared (m/s²) — velocity changes by that many m/s each second
Positive Acceleration
Velocity increases in the positive direction (speeding up forward)
Negative Acceleration
Velocity decreases or object moves faster in negative direction
Deceleration
Common term for slowing down; acceleration opposes direction of motion
Average vs Instantaneous
Average: over a time interval; Instantaneous: at one exact moment
A car speeds up from 10 m/s to 30 m/s in 5 s. Find its acceleration.
A cyclist slows from 12 m/s to 0 m/s in 4 s. Find the acceleration and describe its direction.
An object has a constant velocity of 8 m/s for 10 s. What is its acceleration?
A rocket accelerates from rest at 15 m/s² for 6 s. What is its final velocity?
A ball rolling down a ramp goes from 2 m/s to 8 m/s in 3 s. Is this positive or negative acceleration? Calculate it.
A train accelerates from 5 m/s to 25 m/s in 10 s. Find its acceleration.
Hint: Use a = (v_f − v_i) / t. Identify v_f, v_i, and t first.
A car brakes from 20 m/s to 8 m/s in 4 s. What is the acceleration? Is it positive or negative?
Hint: Subtract initial velocity from final velocity. A negative result means the object is slowing down.
An object accelerates at 3 m/s² for 7 s starting from rest. What is its final velocity?
Hint: Rearrange the acceleration formula to solve for v_f.
Two cars: Car A goes from 0 to 60 m/s in 10 s; Car B goes from 0 to 60 m/s in 6 s. Which has greater acceleration?
Hint: Calculate acceleration for each and compare.
A ball is thrown upward. As it rises, is its acceleration positive or negative (taking up as positive)?
Hint: Gravity always pulls downward. What direction is the acceleration due to gravity?
Key Vocabulary
Acceleration
The rate of change of velocity over time; a = (v_f − v_i) / t.
Example: A car going from 0 to 20 m/s in 4 s has an acceleration of 5 m/s².
Deceleration
A decrease in speed; acceleration that acts opposite to the direction of motion.
Example: Applying brakes causes deceleration — the car slows down.
Average Acceleration
Total change in velocity divided by total time elapsed over an interval.
Example: A bus that changes velocity by 12 m/s over 3 s has an average acceleration of 4 m/s².
Instantaneous Acceleration
The acceleration of an object at one specific moment in time.
Example: A speedometer reading changing rapidly indicates high instantaneous acceleration.
Interactive Practice — 5 Questions
A car goes from 0 m/s to 20 m/s in 4 s. What is its acceleration?
An object slows from 15 m/s to 5 m/s in 2 s. What is the acceleration?
Which unit correctly expresses acceleration?
An object moves at a constant 10 m/s. Its acceleration is:
Deceleration means the acceleration is:
Independent Practice
A motorcycle accelerates from 5 m/s to 35 m/s in 6 s. Calculate its acceleration.
A skateboarder slows from 8 m/s to 2 m/s in 3 s. Find the acceleration and state whether it is positive or negative.
An airplane accelerates at 4 m/s² for 12 s starting from rest. What is its final velocity?
Explain in your own words the difference between deceleration and negative acceleration. Are they always the same thing?
★ A car accelerates at 3 m/s² for 5 s, then decelerates at 2 m/s² for 4 s. If it started at 10 m/s, what is its final velocity?
ChallengeCommon Mistakes
Thinking deceleration always means negative acceleration.
Deceleration means slowing down. If an object moves in the negative direction and slows, its acceleration is actually positive.
Confusing speed and velocity when calculating acceleration.
Acceleration uses velocity (which has direction), not just speed. Always track direction with a sign.
Math Tips
Always write out a = (v_f − v_i) / t and label each variable before substituting numbers. The sign of the answer tells you the direction of acceleration.