For both SL and HL, solve uniformly accelerated motion problems by choosing a positive direction, listing the known variables, selecting an equation containing the unknown, and solving algebraically. These equations apply only when acceleration is constant.
Use the five kinematic variables: initial velocity , final velocity , acceleration , displacement , and time . Assign signs consistently according to your chosen positive direction.
| Situation | Useful equation |
|---|---|
| Time and both velocities are involved | |
| Displacement, time, and initial velocity are involved | |
| Time is not given or required | |
| Acceleration is not given or required |
Before choosing an equation, confirm that the motion has uniform acceleration. If acceleration changes, these equations cannot describe the whole motion in one step; divide the motion into suitable intervals or use graphical methods. On a velocity-time graph, constant acceleration appears as a straight line: its gradient is acceleration and the area under it is displacement.
A reliable process is:
For example, a ball is thrown vertically upward at . Taking upward as positive gives , at maximum height, and . Using
produces
As a check, gives to reach the top, consistent with a positive upward displacement.
The negative acceleration means that gravity acts downward. A common misconception is that negative acceleration always means slowing down. It does not: the sign shows direction, while speeding up or slowing down depends on the relative directions of velocity and acceleration.
In a Calculate question, show the equation, substitution, and final answer. Define your sign convention clearly, use from the IB Physics data booklet, and do not apply these equations when acceleration varies.
