Acceleration

Acceleration tells us how quickly velocity changes. If something speeds up, slows down, or changes direction, it is accelerating. In straight-line motion, acceleration describes how speed changes each second.

Key idea and formula

Velocity means speed in a chosen direction. Acceleration is the change in velocity per unit time.

$a = \frac{\Delta v}{\Delta t}$ where $\Delta v$ is the change in velocity and $\Delta t$ is the time taken.

• Units: metres per second squared, $\text{m s}^{-2}$.
• Signs matter: positive acceleration increases speed (in the chosen direction); negative acceleration (deceleration) reduces speed or accelerates in the opposite direction.
• Zero acceleration means constant velocity (could be moving or at rest).

Free fall

Near Earth’s surface, objects in free fall accelerate downwards at about $g \approx 9.8\,\text{m s}^{-2}$ (often taken as $10\,\text{m s}^{-2}$ in calculations). Ignoring air resistance, all objects share the same $g$.

Useful relation for straight-line motion: $v = u + a t$ (final velocity = initial velocity + acceleration × time).

Speed–time graphs

• The gradient (slope) gives acceleration. Steeper slope = larger acceleration.
• Horizontal line (zero slope) means constant speed ($a=0$).
• A downward slope means negative acceleration (deceleration).
• The area under the speed–time graph gives distance travelled.

Common misconceptions

• “Zero acceleration means zero speed” — actually, it means constant speed.
• “Heavier objects fall faster (without air)” — in vacuum they share the same $g$.
• “Deceleration is a separate idea” — it is just negative acceleration.