Physics / Unit 1: Motion in One Dimension
1.3 Acceleration
Notes
Acceleration is the rate at which velocity changes: $\displaystyle a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}$.
- Unit: $\text{m/s}^2$ (meters per second, every second).
- An object accelerates when it speeds up, slows down or changes direction.
- If acceleration points opposite the velocity, the object slows down (sometimes called deceleration).
- Example: a car goes from $5 \text{ m/s}$ to $25 \text{ m/s}$ in 4 s: $\displaystyle a = \frac{25 - 5}{4} = 5 \text{ m/s}^2$.
Practice
A skateboarder speeds up from $2 \text{ m/s}$ to $8 \text{ m/s}$ in 3 s. What is her acceleration?
$\displaystyle a = \frac{8 - 2}{3} = 2 \text{ m/s}^2$.
A car moving at $30 \text{ m/s}$ brakes to a stop in 5 s. What is its acceleration?
$\displaystyle a = \frac{0 - 30}{5} = -6 \text{ m/s}^2$; negative means opposite the motion.
A car drives around a curve at a constant speed of $15 \text{ m/s}$. Is it accelerating?
Velocity includes direction, so a change in direction is a change in velocity.
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