ACCELERATION – UNDERSTANDING THE RATE OF CHANGE OF VELOCITY
Prepared by: Ma. Johanna B. Testa, LPT
LEARNING OBJECTIVES
- Define acceleration and its vector nature
- Differentiate average vs. instantaneous acceleration
- Use formulas to solve real-world problems
- Interpret acceleration in motion graphs and circular motion
WHAT IS ACCELERATION?
Any change in velocity—due to speeding up, slowing down, or changing direction—is acceleration
Acceleration is a vector (has magnitude and direction)
DEFINITIONS
Rate at which velocity changes with time
Includes speed and direction changes
Uniform acceleration: constant rate of velocity change
CONSTANT SPEED
The object moves the same distance in every equal time interval.
There is no change in velocity, so acceleration is zero.
The object could still be moving (motion is occurring), but it’s not speeding up or slowing down.
Example:
A car driving at 60 km/h on a straight road — every 10 minutes, it covers exactly 10 km.
From Khan Academy:
“If velocity is constant, then the acceleration is zero — there’s no change in how fast or slow the object moves or in which direction.”
CONSTANT ACCELERATION
The object’s velocity is changing at a steady rate — either increasing or decreasing by the same amount per unit time.
The object travels different distances in each equal time interval.
Example:
A ball dropped from rest falls with a constant acceleration of 9.8 m/s² (ignoring air resistance).
After 1 second: speed = 9.8 m/s
After 2 seconds: speed = 19.6 m/s
Distance covered increases more each second
From McGraw-Hill Physical Science:
“Constant acceleration means that the velocity of an object changes by the same amount each second.”
FORMULAE
Average Acceleration: a = (vf - vi) / Δt
Units: m/s²
EXPLANATION
Acceleration occurs when speed or direction (or both) changes
Speeding up: velocity and acceleration same direction
Slowing down: opposite directions
Turning: acceleration toward center of curve
VISUALIZING ACCELERATION
Diagrams: velocity and acceleration vectors in three cases
Show speeding up, slowing down, turning cases with arrows
SAMPLE CALCULATIONS
1. Car: 7 m/s to 16 m/s in 5 s → a
2. Bicycle: 1 m/s to 5 m/s in 3 s → a
3. A car starts at 7 m/s and accelerates at 1.8 m/s² for 5 seconds. What is its final velocity?
4. A car accelerates from 7 m/s to 16 m/s at a constant rate of 1.8 m/s². How much time did this take?
SPEED-TIME GRAPHS
Horizontal line: constant speed (zero acceleration)
Upward slope: speeding up (positive acceleration)
Downward slope: slowing down (negative acceleration)
Direction changes are not shown on speed-time graphs
ACCELERATION IN DAILY LIFE
Car braking, rollercoaster drop, turning corner
Free-fall near Earth: approx. 9.8 m/s² downward
SUMMARY TABLE
Concept | Equation | Example
Average acceleration | (vf - vi)/Δt | Car speeding/slowing
Instantaneous | dv/dt | Quickest change moment
Centripetal | Direction change | Car turning a bend
PRACTICE QUESTIONS
1. Bus: 5 m/s to 20 m/s in 10 s → ?
2. Object: 12 m/s to 4 m/s in 4 s → ?
REFERENCES
McGraw‑Hill Physical Science, Lesson 3: Acceleration
Khan Academy: What is acceleration?
Britannica: Acceleration (updated 2025)