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: scalars and vectors, the equations of motion, and the two graphs that capture it all.

Scalars and vectors 🧭

A **scalar** has only **size**; a **vector** has size **and direction**. • **Distance** (how far you travel) and **speed** are **scalars**. • **Displacement** (distance in a straight line from the start, with direction) and **velocity** (speed in a given direction) are **vectors**.

Match each quantity to its meaning

Spot the vectors

Select ALL THREE of these quantities that are vectors (they have a direction).

• Displacement
• Velocity
• Acceleration
• Distance
• Speed
• Time

Going in circles 🔄

Because velocity is a vector, it changes if **either** the speed **or** the direction changes. **(Higher tier)** An object moving in a circle at a **constant speed** still has a **continuously changing velocity**, because its direction is always changing. A changing velocity is an acceleration — so a **resultant force** is needed to keep it moving in the circle.

Round the roundabout

A car drives around a roundabout at a steady 10 m/s. Is it accelerating?

• Yes — its direction keeps changing, so its velocity changes, which is an acceleration
• No — its speed is constant, so it cannot be accelerating
• No — acceleration only happens when moving in a straight line
• Only at the exact moment it enters the roundabout

How fast? 🚶

**Speed** is how fast something moves. Some typical values worth knowing: • Walking ≈ **1.5 m/s** • Running ≈ **3 m/s** • Cycling ≈ **6 m/s** • A car ≈ **25 m/s** Sound travels through air at about **330 m/s**. Real speeds vary with age, fitness, terrain and wind.

Match each to its typical speed

Find the speed

An interactive activity.

Distance-time graphs 📈

On a **distance-time graph**, the **gradient (steepness) is the speed**: a steeper line means a faster object, and a **flat, horizontal line means the object is stationary**. **(Higher tier)** A curved line means the speed is changing (accelerating); the speed at an instant is the gradient of the **tangent** to the curve.

Plot the journey

An interactive activity.

Acceleration 🚀

**Acceleration** measures how quickly velocity changes: **a = Δv / t** (change in velocity ÷ time taken), measured in **m/s²**. Speeding up is a positive acceleration; slowing down is a negative acceleration (a deceleration).

Find the acceleration

An interactive activity.

The motion equation ⚗️

For **uniform (constant) acceleration**, a given equation links the velocities, acceleration and distance: **v² − u² = 2 a s** where u = starting velocity, v = final velocity, a = acceleration and s = distance travelled.

Find the final velocity

An interactive activity.

Velocity-time graphs 📉

On a **velocity-time graph**, two things matter: • the **gradient is the acceleration** • the **area under the line is the distance travelled** Take care — these mean different things from a distance-time graph, where the gradient is the speed.

Distance from a velocity-time graph

An interactive activity.

Distance under the line

An interactive activity.

Which graph is which?

Select ALL THREE statements about motion graphs that are TRUE.

• On a distance-time graph, the gradient is the speed
• On a velocity-time graph, the gradient is the acceleration
• On a velocity-time graph, the area under the line is the distance
• On a distance-time graph, the area under the line is the speed
• On a velocity-time graph, the gradient is the distance
• On a distance-time graph, a flat line means constant speed

Motion summary

Distance and speed are _____, while displacement and velocity are vectors because they have direction. On a distance-time graph the gradient is the _____. Acceleration is a = Δv ÷ _____. On a velocity-time graph, the area under the line is the _____ travelled.