# Collisions

• Philip Dyke
• Roger Whitworth
Chapter
Part of the Macmillan Mathematical Guides book series (MG)

## Abstract

In Chapter 3, the term momentum was defined as the product of mass and velocity. It has particular significance when we study collisions. Let us demonstrate this with a simple example. A heavy lorry and a car are travelling side by side at the same speed and need to stop at a red light. Common experience leads us to expect that the braking force required to bring the lorry to a stop must be greater than that required to stop the lighter car. Newton’s second law states that:
$$force = mass\,\; \times \,\frac{{d(velocity)}}{{dt}}$$
or, for constant mass:
$$force = \,\frac{{d(mass\,\; \times velocity)}}{{dt}}$$
The right-hand side of this equation represents the rate of change of momentum. Hence, the lorry, which has the larger momentum, needs a greater force to make it stop than does the car.

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© Philip Dyke & Roger Whitworth 1992

## Authors and Affiliations

• Philip Dyke
• 1
• Roger Whitworth
• 2
1. 1.Polytechnic South WestUK
2. 2.Droitwich High SchoolUK