IGCSE Physics 0625

1.2 Motion - Deceleration

This section focuses on understanding deceleration, which is a type of acceleration. We will explore its definition and how to apply it in physics calculations.

What is Deceleration?

Deceleration refers to a decrease in the speed of an object. It is often described as negative acceleration because it involves a change in velocity where the velocity is becoming less negative (for a negative velocity) or more positive (for a positive velocity).

Relationship between Deceleration and Acceleration

Deceleration is simply acceleration with a negative value. In physics equations, we treat it the same as acceleration, but the sign indicates the direction of the change in velocity.

Formulae for Deceleration

The fundamental equation relating velocity, acceleration (including deceleration), and time is:

$$v = u + at$$

Where:

• v = final velocity
• u = initial velocity
• a = acceleration (can be positive or negative)
• t = time

If an object is decelerating, the acceleration will be negative. Therefore, we can write the formula as:

$$v = u - at$$

Examples and Calculations

Let's consider some examples to illustrate how to use these formulae with deceleration.

Example 1: Braking Car

A car is travelling at 20 m/s and decelerates at a rate of 4 m/s². How long does it take for the car to come to a stop?

Here, the initial velocity (u) = 20 m/s, the final velocity (v) = 0 m/s, and the acceleration (a) = -4 m/s² (deceleration).

Using the formula: $$v = u - at$$

$$0 = 20 - (-4)t$$

$$0 = 20 + 4t$$

$$4t = -20$$

$$t = -5 \text{ seconds}$$

The time is calculated as negative because the deceleration is in the opposite direction to the initial motion.

Example 2: Stopping Distance

A cyclist is travelling at 10 m/s and brakes with a deceleration of 2 m/s². Calculate the distance travelled during braking.

Initial velocity (u) = 10 m/s, deceleration (a) = -2 m/s². We need to find the distance travelled (s). We can use the following equation:

$$v^2 = u^2 + 2as$$

Since the final velocity (v) is 0 m/s (the cyclist stops):

$$0 = 10^2 + 2(-2)s$$

$$0 = 100 - 4s$$

$$4s = 100$$

$$s = 25 \text{ metres}$$

Summary

Deceleration is a negative acceleration that causes a decrease in the speed of an object. It can be easily incorporated into the standard motion equations by treating it as a negative value for acceleration. Understanding deceleration is crucial for analyzing situations involving braking, stopping distances, and other scenarios where an object's velocity is decreasing.

Concept	Description
Deceleration	A decrease in the speed of an object.
Negative Acceleration	Acceleration in the opposite direction to the motion.
Formula	$$v = u - at$$ (where 'a' is negative for deceleration)