Forces in Motion

Forces in Motion

Before you can explain WHY things move, you have to describe HOW they move: how far, how fast, and how quickly that speed changes. This module builds the toolkit, and it turns on one idea that sounds like a contradiction: an object can be accelerating hard while its speedometer never moves.

Scalars and vectors

The difference sounds like bookkeeping and is not. The last row is where it starts to matter:

Round the roundabout

A car drives all the way round a roundabout at a steady 10 m/s, and its speedometer never moves. Is it accelerating?

• Yes. Its direction is changing continuously, so its velocity is changing, and a changing velocity is an acceleration
• No. Its speed is constant, so nothing about its motion is changing
• No. Acceleration only applies to motion in a straight line
• Only at the instant it enters and the instant it leaves the roundabout

How fast is fast?

Exam questions expect you to know roughly how fast everyday things move, and to spot an answer that cannot be right:

How far away?

At a firework display you see a flash and hear the bang 2 seconds later. Sound travels through air at about 330 m/s. Roughly how far away was the firework?

• About 660 m, because the sound covered 330 metres in each of the two seconds
• About 165 m, dividing the speed by the two seconds
• About 330 m, since that is how far sound travels
• It cannot be estimated without knowing the speed of light as well

The two graphs

Both plot time across the bottom, and the same feature means different things on each. This is the single most examined confusion in the topic. Distance-time graph • Gradient = the speed. Steeper means faster. • A horizontal line means stationary. • A curve means the speed is changing. (Higher tier: the speed at an instant is the gradient of the tangent.) • The area underneath means nothing useful at all. Velocity-time graph • Gradient = the acceleration. • A horizontal line means constant velocity, which is still moving. • The area under the line = the distance travelled.

Plot the journey

This distance-time graph is a straight line through the origin: the object moves a steady 2 metres every second. Plot the point for a time of 3 seconds.

What does each feature mean?

Find the acceleration

A car speeds up from rest to 20 m/s in 5 s. What is its acceleration, in m/s²?

When there is no time given

Sometimes a question gives you a distance but no time, and then a = Δv ÷ t is no use. That is what the given equation is for: v² − u² = 2 a s where u is the starting velocity, v the final velocity, a the acceleration and s the distance. A cyclist already travelling at 6 m/s accelerates at 4 m/s² over 8 m. Then v² = u² + 2as = 36 + 64 = 100, so v = 10 m/s. Note the u² term: starting from rest it vanishes, and starting from anything else it does not. Forgetting to add it is the standard error, and it always makes the answer too small.

Find the final velocity

A train is already moving at 5 m/s when it accelerates at 2 m/s² over a distance of 36 m. What is its final velocity, in m/s?

Distance under the line

On a velocity-time graph, an object travels at a steady 10 m/s for 8 s, so the shape under the line is a rectangle. What distance does it travel, in metres?

Which are true?

Select ALL THREE statements that are TRUE.

• An object can be accelerating even though its speed never changes, provided its direction is changing
• The gradient means different things on the two graphs, and only the velocity-time graph has a useful area
• v² − u² = 2as is the equation to reach for when a question gives you a distance but no time
• A horizontal line on a distance-time graph means the object is moving at a constant speed
• The area under a distance-time graph gives the distance travelled
• Speed and velocity are two words for the same quantity

Motion summary

Distance and speed are _____, while displacement and velocity are vectors, which is why an object going round a bend at constant speed is still _____. On a distance-time graph the gradient is the speed and a horizontal line means the object is _____. On a velocity-time graph the gradient is the acceleration and the area under the line is the distance. When a question gives a distance but no time, use v² − u² = 2 a _____.