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[accordion title=”1. Definitions”]
- Displacement is the distance travelled along a specified direction.
- Speed is the rate of change of distance travelled.
- Velocity is the rate of change of displacement.
- Acceleration is the rate of change of velocity.
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[accordion title=”2. One-Dimensional Motion with Constant Acceleration”]
- $$v=u+at$$
- $$s=(\frac{u+v}{2})t$$
- $$s=ut+\frac{1}{2}at^2$$
- $$v^2=u^2+2as$$
s: displacement
u: initial velocity
v: final velocity
a: acceleration
t: time
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[accordion title=”3. Two-Dimensional Motion”]
- Tip: Sometimes, you will require two equations to solve a kinematics problem. For a parabolic path in a projectile motion without resistive forces, you can draw a table such as the one below and fill in the blank with the information given in the question.
- In the case where a projectile is launched at an angle $$\theta$$ to the horizontal and undergoes the acceleration of free fall, the various horizontal and vertical components of displacement, velocity and acceleration can be expressed in the following way:
| Horizontal | Vertical | |
| displacement, s | $$(u \cos \theta)t$$ | $$(u \sin \theta)t+\frac{1}{2}gt^2$$ |
| initial velocity, u | $$u \cos \theta$$ | $$u \sin \theta$$ |
| initial velocity, v | $$u \cos \theta$$ | $$u \sin \theta +gt$$ |
| acceleration, a | 0 | $$g$$ |
| time, t | same for | both dimensions |
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