Acceleration describes how quickly velocity changes, so it is central to understanding motion in vehicles, falling objects, sports, and machines. Uniform acceleration means the acceleration stays constant, so velocity changes by equal amounts in equal time intervals. Non-uniform acceleration means the acceleration changes with time, so velocity may increase, decrease, or vary irregularly.
Comparing these two cases helps students choose the correct equations and interpret motion graphs accurately.
For uniform acceleration, position-time graphs are curved, velocity-time graphs are straight lines, and acceleration-time graphs are horizontal lines. The SUVAT equations apply only when acceleration is constant over the time interval being analyzed. For non-uniform acceleration, the slope of the velocity-time graph changes, and the area under the acceleration-time graph gives the change in velocity.
In more advanced problems, non-uniform motion is handled by breaking the motion into small intervals, using graphs, or applying calculus.
Key Facts
- Acceleration is the rate of change of velocity: a = Δv / Δt.
- Uniform acceleration means a is constant, so velocity changes by equal amounts in equal time intervals.
- Non-uniform acceleration means a changes with time, so the velocity-time graph is not a straight line.
- For constant acceleration, v = u + at, s = ut + 1/2 at^2, and v^2 = u^2 + 2as.
- On a velocity-time graph, slope equals acceleration and area under the graph equals displacement.
- On an acceleration-time graph, area under the graph equals change in velocity: Δv = area under a-t graph.
Vocabulary
- Acceleration
- Acceleration is the change in velocity per unit time.
- Uniform acceleration
- Uniform acceleration is motion in which acceleration remains constant throughout the time interval.
- Non-uniform acceleration
- Non-uniform acceleration is motion in which acceleration changes with time.
- Velocity-time graph
- A velocity-time graph shows how velocity changes over time, with its slope representing acceleration.
- SUVAT equations
- SUVAT equations are motion equations that relate displacement, initial velocity, final velocity, acceleration, and time when acceleration is constant.
Common Mistakes to Avoid
- Using SUVAT equations for changing acceleration is wrong because those equations assume acceleration is constant over the whole interval.
- Confusing velocity with acceleration is wrong because velocity tells how fast position changes, while acceleration tells how fast velocity changes.
- Reading the height of a velocity-time graph as acceleration is wrong because acceleration is given by the slope of the velocity-time graph.
- Assuming curved position-time graphs always mean changing acceleration is wrong because constant acceleration also produces a curved position-time graph.
Practice Questions
- 1 A cart starts from rest and accelerates uniformly at 2.0 m/s^2 for 6.0 s. Find its final velocity and displacement.
- 2 A car's velocity changes from 4 m/s to 16 m/s in 3 s, then from 16 m/s to 20 m/s in the next 5 s. Find the acceleration in each interval and decide whether the acceleration is uniform.
- 3 A velocity-time graph is a straight rising line for one object and a curved rising line for another. Explain which object has uniform acceleration and how you know.