Year 11 / Linear motion and force
Trade height for motion.
Work is energy transferred by a force acting through a displacement. For a constant force parallel to displacement, W = Fs. Net work changes kinetic energy. Near Earth, raising a mass changes gravitational potential energy by mgΔh.
When resistive effects are negligible, mechanical energy is conserved. With friction, some mechanical energy becomes internal energy. In an elastic collision, both total momentum and total kinetic energy are conserved; in an inelastic one, only the momentum rule remains if external impulse is negligible.
Height becomes speed
Explore the relationship
Released from rest; no drag or friction.
Final speed / m s⁻¹
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Vertical drop / m | Final speed / m s⁻¹ |
|---|---|---|
| Final speed / m s⁻¹ | 0 | 0 |
| Final speed / m s⁻¹ | 0.166667 | 1.80739 |
| Final speed / m s⁻¹ | 0.333333 | 2.55604 |
| Final speed / m s⁻¹ | 0.5 | 3.1305 |
| Final speed / m s⁻¹ | 0.666667 | 3.61478 |
| Final speed / m s⁻¹ | 0.833333 | 4.04145 |
| Final speed / m s⁻¹ | 1 | 4.42719 |
| Final speed / m s⁻¹ | 1.16667 | 4.78191 |
| Final speed / m s⁻¹ | 1.33333 | 5.11208 |
| Final speed / m s⁻¹ | 1.5 | 5.42218 |
| Final speed / m s⁻¹ | 1.66667 | 5.71548 |
| Final speed / m s⁻¹ | 1.83333 | 5.99444 |
| Final speed / m s⁻¹ | 2 | 6.26099 |
| Final speed / m s⁻¹ | 2.16667 | 6.51665 |
| Final speed / m s⁻¹ | 2.33333 | 6.76264 |
| Final speed / m s⁻¹ | 2.5 | 7 |
| Final speed / m s⁻¹ | 2.66667 | 7.22957 |
| Final speed / m s⁻¹ | 2.83333 | 7.45207 |
| Final speed / m s⁻¹ | 3 | 7.66812 |
| Final speed / m s⁻¹ | 3.16667 | 7.87824 |
| Final speed / m s⁻¹ | 3.33333 | 8.0829 |
| Final speed / m s⁻¹ | 3.5 | 8.28251 |
| Final speed / m s⁻¹ | 3.66667 | 8.47742 |
| Final speed / m s⁻¹ | 3.83333 | 8.66795 |
| Final speed / m s⁻¹ | 4 | 8.85438 |
| Final speed / m s⁻¹ | 4.16667 | 9.03696 |
| Final speed / m s⁻¹ | 4.33333 | 9.21593 |
| Final speed / m s⁻¹ | 4.5 | 9.39149 |
| Final speed / m s⁻¹ | 4.66667 | 9.56382 |
| Final speed / m s⁻¹ | 4.83333 | 9.73311 |
| Final speed / m s⁻¹ | 5 | 9.89949 |
| Final speed / m s⁻¹ | 5.16667 | 10.0631 |
| Final speed / m s⁻¹ | 5.33333 | 10.2242 |
| Final speed / m s⁻¹ | 5.5 | 10.3827 |
| Final speed / m s⁻¹ | 5.66667 | 10.5388 |
| Final speed / m s⁻¹ | 5.83333 | 10.6927 |
| Final speed / m s⁻¹ | 6 | 10.8444 |
| Final speed / m s⁻¹ | 6.16667 | 10.9939 |
| Final speed / m s⁻¹ | 6.33333 | 11.1415 |
| Final speed / m s⁻¹ | 6.5 | 11.2872 |
| Final speed / m s⁻¹ | 6.66667 | 11.431 |
| Final speed / m s⁻¹ | 6.83333 | 11.573 |
| Final speed / m s⁻¹ | 7 | 11.7132 |
| Final speed / m s⁻¹ | 7.16667 | 11.8519 |
| Final speed / m s⁻¹ | 7.33333 | 11.9889 |
| Final speed / m s⁻¹ | 7.5 | 12.1244 |
| Final speed / m s⁻¹ | 7.66667 | 12.2583 |
| Final speed / m s⁻¹ | 7.83333 | 12.3909 |
| Final speed / m s⁻¹ | 8 | 12.522 |
| Final speed / m s⁻¹ | 8.16667 | 12.6517 |
| Final speed / m s⁻¹ | 8.33333 | 12.7802 |
| Final speed / m s⁻¹ | 8.5 | 12.9074 |
| Final speed / m s⁻¹ | 8.66667 | 13.0333 |
| Final speed / m s⁻¹ | 8.83333 | 13.158 |
| Final speed / m s⁻¹ | 9 | 13.2816 |
| Final speed / m s⁻¹ | 9.16667 | 13.404 |
| Final speed / m s⁻¹ | 9.33333 | 13.5253 |
| Final speed / m s⁻¹ | 9.5 | 13.6455 |
| Final speed / m s⁻¹ | 9.66667 | 13.7647 |
| Final speed / m s⁻¹ | 9.83333 | 13.8828 |
| Final speed / m s⁻¹ | 10 | 14 |
Explore: Increase the starting height and compare final speed with energy.
A 2 kg object speeds up from 3 to 5 .
- Net work = 0.5 × 2 × ( − ).
- Net work = 16 J.
Assumed knowledge
Squaring velocities.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Use work–energy relationships.
- Distinguish elastic and inelastic collisions.
READY TO TRY IT?