Year 11 / Linear motion and force
Keep the signs consistent.
The constant-acceleration equations connect initial velocity, final velocity, time and displacement. Choose a positive direction first and assign signs consistently. These equations are valid only while acceleration is constant.
In free fall near Earth, acceleration is approximately constant downward. At the top of a vertical throw, velocity is instantaneously zero but acceleration remains downward. Ignoring drag, objects of different masses have the same gravitational acceleration.
Velocity and acceleration
Explore the relationship
Initial velocity +3 m s⁻¹; constant acceleration. The graph area gives signed displacement.
Velocity / m s⁻¹
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Time / s | Velocity / m s⁻¹ |
|---|---|---|
| Velocity / m s⁻¹ | 0 | 3 |
| Velocity / m s⁻¹ | 0.133333 | 3.13333 |
| Velocity / m s⁻¹ | 0.266667 | 3.26667 |
| Velocity / m s⁻¹ | 0.4 | 3.4 |
| Velocity / m s⁻¹ | 0.533333 | 3.53333 |
| Velocity / m s⁻¹ | 0.666667 | 3.66667 |
| Velocity / m s⁻¹ | 0.8 | 3.8 |
| Velocity / m s⁻¹ | 0.933333 | 3.93333 |
| Velocity / m s⁻¹ | 1.06667 | 4.06667 |
| Velocity / m s⁻¹ | 1.2 | 4.2 |
| Velocity / m s⁻¹ | 1.33333 | 4.33333 |
| Velocity / m s⁻¹ | 1.46667 | 4.46667 |
| Velocity / m s⁻¹ | 1.6 | 4.6 |
| Velocity / m s⁻¹ | 1.73333 | 4.73333 |
| Velocity / m s⁻¹ | 1.86667 | 4.86667 |
| Velocity / m s⁻¹ | 2 | 5 |
| Velocity / m s⁻¹ | 2.13333 | 5.13333 |
| Velocity / m s⁻¹ | 2.26667 | 5.26667 |
| Velocity / m s⁻¹ | 2.4 | 5.4 |
| Velocity / m s⁻¹ | 2.53333 | 5.53333 |
| Velocity / m s⁻¹ | 2.66667 | 5.66667 |
| Velocity / m s⁻¹ | 2.8 | 5.8 |
| Velocity / m s⁻¹ | 2.93333 | 5.93333 |
| Velocity / m s⁻¹ | 3.06667 | 6.06667 |
| Velocity / m s⁻¹ | 3.2 | 6.2 |
| Velocity / m s⁻¹ | 3.33333 | 6.33333 |
| Velocity / m s⁻¹ | 3.46667 | 6.46667 |
| Velocity / m s⁻¹ | 3.6 | 6.6 |
| Velocity / m s⁻¹ | 3.73333 | 6.73333 |
| Velocity / m s⁻¹ | 3.86667 | 6.86667 |
| Velocity / m s⁻¹ | 4 | 7 |
| Velocity / m s⁻¹ | 4.13333 | 7.13333 |
| Velocity / m s⁻¹ | 4.26667 | 7.26667 |
| Velocity / m s⁻¹ | 4.4 | 7.4 |
| Velocity / m s⁻¹ | 4.53333 | 7.53333 |
| Velocity / m s⁻¹ | 4.66667 | 7.66667 |
| Velocity / m s⁻¹ | 4.8 | 7.8 |
| Velocity / m s⁻¹ | 4.93333 | 7.93333 |
| Velocity / m s⁻¹ | 5.06667 | 8.06667 |
| Velocity / m s⁻¹ | 5.2 | 8.2 |
| Velocity / m s⁻¹ | 5.33333 | 8.33333 |
| Velocity / m s⁻¹ | 5.46667 | 8.46667 |
| Velocity / m s⁻¹ | 5.6 | 8.6 |
| Velocity / m s⁻¹ | 5.73333 | 8.73333 |
| Velocity / m s⁻¹ | 5.86667 | 8.86667 |
| Velocity / m s⁻¹ | 6 | 9 |
| Velocity / m s⁻¹ | 6.13333 | 9.13333 |
| Velocity / m s⁻¹ | 6.26667 | 9.26667 |
| Velocity / m s⁻¹ | 6.4 | 9.4 |
| Velocity / m s⁻¹ | 6.53333 | 9.53333 |
| Velocity / m s⁻¹ | 6.66667 | 9.66667 |
| Velocity / m s⁻¹ | 6.8 | 9.8 |
| Velocity / m s⁻¹ | 6.93333 | 9.93333 |
| Velocity / m s⁻¹ | 7.06667 | 10.0667 |
| Velocity / m s⁻¹ | 7.2 | 10.2 |
| Velocity / m s⁻¹ | 7.33333 | 10.3333 |
| Velocity / m s⁻¹ | 7.46667 | 10.4667 |
| Velocity / m s⁻¹ | 7.6 | 10.6 |
| Velocity / m s⁻¹ | 7.73333 | 10.7333 |
| Velocity / m s⁻¹ | 7.86667 | 10.8667 |
| Velocity / m s⁻¹ | 8 | 11 |
Explore: Use negative acceleration and locate when the velocity passes through zero.
A cart starts at 3 and accelerates at 2 for 4 s.
- v = 3 + 2 × 4 = 11 .
- s = 3 × 4 + 0.5 × 2 × = 28 m.
Assumed knowledge
Solving equations and squares.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Solve constant-acceleration motion.
- Model free fall without air resistance.
READY TO TRY IT?