Velocity and acceleration: Revision

1. Velocity (v⃗\vec{v})

• Definition: The rate of change of displacement.
• Vector quantity (has both magnitude and direction).
• Formula:

where: $\vec{v}_{\text{average}} = \frac{\Delta x}{\Delta t}$

• $\Delta x$ = displacement $(m)$
• $\Delta t$ = time interval $(s)$
• Speed $(s)$ is a scalar and does not consider direction.

2. Acceleration $(\vec{a})$

• Definition: The rate of change of velocity.
• Vector quantity.
• Formula:

where: $\vec{a} = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}$

• $v_f$ = final velocity $(m/s)$
• $v_i$ = initial velocity $(m/s)$
• $\Delta v$ = change in velocity

3. Equations of Motion

These equations describe the relationships between velocity, acceleration, displacement, and time:

1. $v_f = v_i + a \Delta t$
2. $v_f^2 = v_i^2 + 2a \Delta x$
3. $\Delta x = v_i \Delta t + \frac{1}{2} a \Delta t^2$

4. Key Takeaways

• Velocity is a vector; speed is a scalar.
• Acceleration occurs when velocity changes.
• Equations of motion are provided in the exam data sheet, but you must know how to use them.