Acceleration

A car that goes from 0 to 100 km/h in 10 seconds gains about 2.8 m/s of speed every second.

Acceleration is change in velocity per second

When you press the accelerator, the car’s velocity changes. Acceleration measures how quickly that happens: a = Δv ÷ Δt, the change in velocity divided by the time taken. If a car goes from 0 to 27.8 m/s (100 km/h) in 10 s, its average acceleration is 27.8 ÷ 10 ≈ 2.8 m/s per second. We write the unit as m/s², read "metres per second squared", but it helps to say it the long way: every second, the velocity changes by 2.8 m/s.

Acceleration is a vector. If you choose forward as positive, speeding up forward gives a positive acceleration and braking gives a negative one. A car that slows from 20 m/s to 0 in 4 s has a = (0 − 20) ÷ 4 = −5 m/s². People often call this deceleration, but in physics it is acceleration with a minus sign. Careful: a negative acceleration does not always mean slowing down. A car reversing faster and faster has a negative velocity and a negative acceleration, and it is speeding up.

Turning is accelerating too

Because velocity includes direction, changing direction is also acceleration. A ball on a string whirled in a circle at steady speed is accelerating towards the centre all the time. The ball in the motion lab shows another case. Its horizontal velocity stays the same, but its vertical velocity changes by the same amount every second, so the ball accelerates downward the whole flight, even at the very top where it is moving sideways.

Equations for steady acceleration

When the acceleration stays constant, a few short equations describe the motion. Velocity after time t: v = v₀ + a t. Displacement after time t: d = v₀ t + ½ a t². Starting from rest, these become v = a t and d = ½ a t². A car accelerating from rest at 3 m/s² reaches 3 × 6 = 18 m/s after 6 s and has covered ½ × 3 × 6² = 54 m. Notice the t² in the distance: double the time and the distance becomes four times larger, because the car is also going faster in the second half.

Acceleration is something you can feel. When a lift starts upwards you feel heavier for a moment, and when it slows at the top you feel lighter. When a bus pulls away, you lean backwards; when it brakes, you lurch forwards. You do not feel steady speed at all: in a smooth plane at cruising speed you can pour a drink without spilling it. Your body senses changes in velocity, not velocity itself, which is a first hint of Newton’s first law in the Forces course.