Deceleration and Negative Acceleration

Deceleration means the speed of an object is decreasing. In calculations, deceleration appears as a negative acceleration when the object slows down in the positive direction.

What is the difference between deceleration and negative acceleration?

Deceleration specifically means “slowing down”. Negative acceleration means the acceleration vector points in the negative direction. These are the same thing when the object moves in the positive direction.

A car moving north at 20 m/s that brakes to rest has:

• Speed change: from 20 m/s to 0 m/s
• Acceleration: $a = \frac{0 - 20}{t}$, which is negative
• The car is decelerating

Worked example

A train travelling at 30 m/s applies its brakes and stops in 15 s. Calculate the deceleration. [3]

Step 1. $a = \frac{v - u}{t}$

Step 2. $a = \frac{0 - 30}{15} = \frac{-30}{15}$

Step 3. $a = -2.0\ \text{m/s}^2$

The deceleration is 2.0 m/s² (positive value, because deceleration is the magnitude of the negative acceleration).

Marking points: M1 for equation. M1 for correct substitution with 0 as final velocity. A1 for magnitude 2.0 m/s² (accept −2.0 m/s² with negative sign explained).

These marking points are for this original example and are not an official Cambridge mark scheme.

Common errors and how to correct them

• Subtracting the wrong way round. Calculate $v - u$, not $u - v$. The initial velocity is subtracted from the final velocity.
• Confusing the sign. If the question asks for deceleration, give a positive magnitude. If it asks for acceleration, include the negative sign. Read the question carefully.
• Assuming deceleration means the object stops. An object can decelerate and still be moving. Deceleration only means the speed is reducing, not that it has reached zero.

How to apply this in an exam

When a question says “calculate the deceleration”, it expects a positive value. When it says “calculate the acceleration”, include the negative sign to show the object is slowing. State the unit m/s² in both cases.