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Displacement under constant acceleration calculator
Motion
Gives displacement from initial velocity, acceleration and time.
s = u t + ½ a t2
This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equations = u t + ½ a t2
- Substitute the valuess = 3 × 5 + ½ × 2 × 52
- Calculates = 40 m
- Give the answer to 3 significant figuress = 40.0 m
Worked example
Find s, the displacement. Given: initial velocity u = 3.00 m/s; acceleration a = 2.00 m/s²; time t = 5.00 s.
- Write the equations = u t + ½ a t2
- Substitute the valuess = 3 × 5 + ½ × 2 × 52
- Calculates = 40 m
- Give the answer to 3 significant figuress = 40.0 m
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| s | Displacement | m |
| u | Initial velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | s |
Displacement under constant acceleration: rearranged
- To find displacement: s = u t + ½ a t2
- To find initial velocity: u = (s − ½ a t2) / t
- To find acceleration: a = 2(s − u t) / t2
- To find time: t = (−u + √(u2 + 2a s)) / a
Exam tip
Solving for time means solving a quadratic. This calculator gives the positive root. Check whether the other root has a physical meaning.
Common questions
What is the formula for displacement under constant acceleration?
The equation is s = u t + ½ a t², where s is the displacement (m); u is the initial velocity (m/s); a is the acceleration (m/s²); t is the time (s).
What units should I use for displacement under constant acceleration?
In SI units: displacement in m, initial velocity in m/s, acceleration in m/s², time in s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange s = u t + ½ a t²?
Rearranging gives these forms: to find displacement: s = u t + ½ a t². to find initial velocity: u = (s − ½ a t²) / t. to find acceleration: a = 2(s − u t) / t². to find time: t = (−u + √(u² + 2a s)) / a.
Practise displacement under constant acceleration questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
More motion equations: Speed, distance and time, Acceleration, Final velocity, Velocity squared, Displacement from average velocity, Momentum, Force and change in momentum, Centripetal force. See the full list on the a-level physics equation calculator page.