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Acceleration Explained

Kinematics

Acceleration is one of the first ideas you meet in kinematics, and it is more subtle than it looks. It does not just mean speeding up: any change in velocity counts, including slowing down and changing direction. A car braking, a ball thrown upward, and a satellite circling Earth are all accelerating, even though their speeds behave very differently.

What acceleration is

Acceleration is the rate of change of velocity with time. Because velocity includes direction, acceleration happens whenever an object speeds up, slows down, or changes direction. Its SI unit is the metre per second squared (m/s²), which means how many metres per second of velocity are gained or lost each second. An acceleration of 5 m/s² means the velocity changes by 5 m/s every second. Acceleration is a vector, so it has a direction: speeding up in the forward direction gives a forward acceleration, while braking gives an acceleration pointing backward.

Calculating acceleration

For motion with constant acceleration, use **a = (v − u) / t**, where u is the initial velocity, v is the final velocity, and t is the time taken. If v is greater than u, the acceleration is positive; if v is less than u, it is negative, which is often called **deceleration**. A velocity-time graph makes this visual: acceleration is the gradient (slope) of the graph. A steep slope means a large acceleration, a flat line means zero acceleration, and a downward slope means deceleration. The area under the graph gives the displacement.

Acceleration in everyday life

You feel acceleration rather than speed: in a smoothly cruising train you feel almost nothing, but you are pressed back into your seat when it pulls away. Gravity gives every falling object near Earth an acceleration of about 9.81 m/s² downward, whatever its mass. A car going around a bend at a steady speed is accelerating because its direction keeps changing, this is centripetal acceleration. Even the Moon is accelerating toward Earth as it orbits, even though its speed barely changes. Whenever velocity changes in size or direction, acceleration is at work.

Common mistakes

• Thinking acceleration only means speeding up. Correction: slowing down and changing direction are accelerations too, because velocity is changing.
• Confusing velocity with acceleration. Correction: a fast object can have zero acceleration (steady speed), and a slow object can have a large acceleration.
• Forgetting that acceleration is a vector. Correction: the sign matters, a negative acceleration means the velocity is decreasing in the chosen positive direction.

Practice questions

1. A cyclist speeds up from 4 m/s to 10 m/s in 3 s. What is the acceleration?
   Show answer

   a = (10 - 4) / 3 = 6 / 3 = 2 m/s².

2. A train slows from 20 m/s to 0 m/s in 10 s. What is its acceleration?
   Show answer

   a = (0 - 20) / 10 = -2 m/s². The negative sign shows it is decelerating.

3. A car travels at a steady 25 m/s around a bend. Is it accelerating?
   Show answer

   Yes, its direction keeps changing, so its velocity changes. It has centripetal acceleration toward the centre of the bend.

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