Acceleration
Understand how velocity changes over time and calculate acceleration
Changing Velocity
From rest to motion
Acceleration is the rate at which velocity changes. It tells us how quickly an object speeds up or slows down. Like velocity, acceleration is a vector quantity—it has both magnitude and direction.
acceleration = change in velocity ÷ time
a = (v - u) / t
where u = initial velocity, v = final velocity, t = time
The SI unit for acceleration is metres per second squared (m/s²). A positive acceleration means the object is speeding up in its direction of motion. A negative acceleration (deceleration) means it's slowing down.
Velocity-time graphs show how an object's velocity changes over time. Two key pieces of information can be extracted:
- Gradient = Acceleration: A steeper slope means greater acceleration. Upward slope = speeding up, downward slope = slowing down.
- Area under graph = Distance: The total area beneath the line equals the distance traveled.
Graph Interpretation
- • Horizontal line = constant velocity (zero acceleration)
- • Straight diagonal line = constant (uniform) acceleration
- • Curved line = changing acceleration
On Earth, all objects experience gravitational acceleration when falling freely. This is approximately:
g ≈ 10 m/s²
(More precisely 9.8 m/s²)
Free fall is when an object falls under gravity with no air resistance. In free fall, all objects accelerate at the same rate regardless of their mass. A feather and a hammer would fall at the same rate in a vacuum.
After 1 second of free fall, an object reaches 10 m/s. After 2 seconds, it reaches 20 m/s, and so on—velocity increases by 10 m/s every second.
Adjust Velocity at Each Time
Calculations
Acceleration (gradient): 5.0 m/s²
Distance (area): 160 m
a = (v - u) / t
Graph Interpretation
- • Horizontal line = constant velocity (no acceleration)
- • Upward slope = acceleration (speeding up)
- • Downward slope = deceleration (slowing down)
- • Area under graph = distance traveled
Acceleration
Question:
A car accelerates uniformly from 5 m/s to 25 m/s in 8 seconds. Calculate: (a) the acceleration, (b) the distance traveled during this time.
Answer:
(a) Acceleration:
a = (v - u) / t
a = (25 - 5) / 8
a = 20 / 8 = 2.5 m/s²
(b) Distance (area under v-t graph):
The graph forms a trapezium. Area = ½ × (sum of parallel sides) × height
Distance = ½ × (5 + 25) × 8
Distance = ½ × 30 × 8 = 120 m
A car accelerates from 0 to 20 m/s in 4 seconds. What is its acceleration?