# 02Predicting constant speed

Mo02PN of the Motion topic
• ## 01 Moving smoothly onMo02PNnugget01 Introduction

### Steady speed

What have an object gliding through space in the farthest corner of the universe (well away from the gravitational pulls of any lurking massive objects) and a car cruising along a straight on the M1 motorway got in common?

Both are moving with a constant speed. In fact they're moving in one direction all the time as well. This restriction to one dimension – everything moving along a single line – results in simple situations where the underlying rules are suitably simple. For more complex situations and rules see the SPT: Force and motion topic.

In the SPT: Forces topic the focus was on the forces acting on a single object. Many of the examples showed objects at rest, with the forces adding to zero. In this episode we'll look at objects moving, but still with the forces acting on that object all adding to zero.

Any moving object could be described as either moving with a constant speed or as having a changing speed. Alice and Charlie and Bob may not agree about the values of the speed that they record, but they will agree as to whether the speed is constant or changing. In this episode you'll concentrate on constant speed. In the next episode you'll look at situations where the speed is not constant: the forces do not add to zero.

The main concern that you'll explore is the essential connection between the constant speed of an object and the forces acting on it.

• ## 02 Equilibrium revisitedMo02PNnugget02 Exposition

### Constant speed when the resultant force is equal to zero

The central idea of this episode is laid out in Newton's first law of motion and can be summarised as follows:

When an object is moving at constant speed there is no resultant force acting on it.

Or alternatively:

When an object is moving at constant speed the resultant force acting on it is zero.

A rather special constant speed is zero: that's what Alice recorded for her handbag, as she was – as seen from both Bob's and Charlie's points of view – co-moving with it. Many of the examples in the SPT: Forces topic, in equilibrium, that just sat beside us on the laboratory bench, with a constant speed of zero, had forces that added to zero.

Now generalise to any constant speed: you can do this by switching to another's point of view. For example, from Alice to Charlie, or from Alice to Bob.

A resultant force of zero might be achieved because there are no forces acting at all (unlikely in the real world, but possible in the farthest corner of the universe).

Alternatively, it might be that there are forces acting but they add to nothing: the resultant force is zero. In the simplest case, there might be a forward driving force and a backwards retarding force. The retarding force is most often a frictional force: some combination of grip, slip and drag. Indeed, in everyday situations when objects are moving, the frictional force is always present to oppose the motion. The frictional force balances the driving force and thereby cancels its effect.

It does not matter whether the value of the speed is 2 m / s, 3 metre / second, 20 metre / second or 40 metre / second, if the speed is constant then the forces add to zero and the retarding force is equal to the driving force. The resultant force is zero.

### Some examples of constant motion

Here is an example of constant motion: a person sliding a heavy box along the ground at a constant speed.

Use the interactive diagram to explore the most significant forces acting on the person, the box and the ground. Notice how the forces acting on the box add to zero, leading to a constant motion.

### The constant speed cyclist

A cyclist moving at a constant speed provides a driving force through the action of their legs, turning the back wheel against the ground, whilst the ground and the air provide retarding forces. When the bicycle is travelling at a constant speed these retarding forces balance the driving force. Use the interactive diagram to see how the forces balance, resulting in motion at a constant speed. (If you doubt that the ground provides retarding forces, try pedalling with a flatter tyre, or across bumpier ground.)

• ## 03 When the resultant force is zeroMo02PNnugget03 Summary

### Zero resultant force predicts a constant speed

When describing the conditions for constant speed the key points are:

• All forces acting on an object add to zero: the resultant force is zero.
• Retarding forces are equal to the driving forces.

Often the retarding forces are the result of friction. It is difficult for us to imagine a world without such frictional forces.

• Friction is a blanket term for the forces that act on moving objects and on objects which we are trying to move.
• When we reduce friction (for example with oil, a cushion of air or a streamlined shape), we find it much easier to make things move or to keep them moving.
• Frictional forces only show up when something is moving (drag or slip) or when a driving force would otherwise accelerate it (grip).
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