GCSE — physicsFoundational7 min read

Speed, Distance, and Time

Calculating speed; distance-time graphs; average vs instantaneous speed

Tutor AI Team
Tutor AI Team

# Speed, Distance, and Time — GCSE Physics

Speed, distance, and time are the most basic quantities used to describe motion. Whether it's a sprinter running 100 m or a planet orbiting the Sun, these quantities allow us to analyse how objects move. Mastering speed calculations and distance-time graphs is essential for GCSE Physics.

1. Speed

Speed tells you how fast an object is moving — the distance it travels per unit of time.

speed=distancetime\boxed{\text{speed} = \frac{\text{distance}}{\text{time}}}

s=dts = \frac{d}{t}

Where:

  • ss = speed (in metres per second, m/s)
  • dd = distance (in metres, m)
  • tt = time (in seconds, s)

Rearranging

d=s×tt=dsd = s \times t \qquad t = \frac{d}{s}

Memory aid: Cover the quantity you want in the triangle:

  • dd on top, ss and tt on the bottom

Units

Quantity SI Unit Common Alternatives
Distance metres (m) km, miles
Time seconds (s) minutes, hours
Speed m/s km/h, mph

Converting Units

km/h to m/s: divide by 3.6 m/s to km/h: multiply by 3.6

Example: 72 km/h = 72÷3.6=2072 \div 3.6 = 20 m/s

2. Speed vs Velocity

Speed Velocity
Scalar (magnitude only) Vector (magnitude + direction)
How fast How fast and in which direction
Always positive Can be positive or negative
Example: 30 m/s Example: 30 m/s north

Why it matters: An object moving in a circle at constant speed has a changing velocity (because direction changes).

3. Average Speed vs Instantaneous Speed

Average Speed

Average speed=total distancetotal time\text{Average speed} = \frac{\text{total distance}}{\text{total time}}

Average speed gives the overall rate of motion for an entire journey. It doesn't tell you about variations in speed along the way.

Example: A car travels 150 km in 2 hours. Average speed=1502=75 km/h\text{Average speed} = \frac{150}{2} = 75 \text{ km/h}

The car might have been faster or slower at different points, but on average it covered 75 km each hour.

Instantaneous Speed

The speed at a particular moment in time. This is what the speedometer in a car shows.

4. Typical Speeds

You should know approximate typical speeds:

Object/Scenario Typical Speed
Walking 1.5 m/s
Running 3 m/s
Cycling 6 m/s
Car in town 13 m/s (≈ 30 mph)
Car on motorway 30 m/s (≈ 70 mph)
Fast train 55 m/s
Speed of sound in air 340 m/s
Aeroplane 250 m/s

Factors that affect speed include: terrain, fitness, wind, traffic, road conditions.

5. Distance-Time Graphs

A distance-time graph shows how the distance travelled changes over time.

Reading the Graph

Feature Meaning
Straight horizontal line Stationary (not moving)
Straight diagonal line (sloping up) Constant speed
Steeper slope Faster speed
Curved line (getting steeper) Accelerating
Curved line (getting flatter) Decelerating

Calculating Speed from a Distance-Time Graph

The gradient (slope) of a distance-time graph equals the speed.

Speed=gradient=change in distancechange in time=ΔdΔt\text{Speed} = \text{gradient} = \frac{\text{change in distance}}{\text{change in time}} = \frac{\Delta d}{\Delta t}

For a Straight Line

The gradient is constant — the speed is constant.

Pick two points on the line: s=d2−d1t2−t1s = \frac{d_2 - d_1}{t_2 - t_1}

For a Curve

The speed is changing. To find the instantaneous speed at a point:

  1. Draw a tangent to the curve at that point
  2. Calculate the gradient of the tangent

Worked Example: Basic Speed Calculation

Problem

Question: A cyclist travels 4500 m in 300 s. Calculate their average speed.

Solution

s=dt=4500300=15 m/ss = \frac{d}{t} = \frac{4500}{300} = 15 \text{ m/s}

Worked Example: Finding Distance

Problem

Question: A car travels at 25 m/s for 120 seconds. How far does it travel?

Solution

d=s×t=25×120=3000 m=3 kmd = s \times t = 25 \times 120 = 3000 \text{ m} = 3 \text{ km}

Worked Example: Finding Time

Problem

Question: A runner needs to cover 1500 m at an average speed of 5 m/s. How long will it take?

Solution

t=ds=15005=300 s=5 minutest = \frac{d}{s} = \frac{1500}{5} = 300 \text{ s} = 5 \text{ minutes}

Worked Example: Multi-Stage Journey

Problem

Question: A student walks 600 m to school in 400 s, then waits at a crossing for 60 s, then walks the remaining 300 m in 200 s. Calculate: (a) The total distance (b) The total time (c) The average speed for the whole journey

Solution

(a) Total distance = 600+300=900600 + 300 = 900 m (b) Total time = 400+60+200=660400 + 60 + 200 = 660 s (c) Average speed = 900/660=1.36900 / 660 = 1.36 m/s

Worked Example: Reading a Distance-Time Graph

Problem

Question: A distance-time graph shows a straight line from (0, 0) to (10, 50). Then a horizontal line from (10, 50) to (15, 50). Then a straight line from (15, 50) to (25, 130).

Calculate: (a) Speed during the first section (b) What happened during the second section (c) Speed during the third section (d) Average speed for the whole journey

Solution

(a) s=50/10=5s = 50/10 = 5 m/s (b) The object was stationary (horizontal line = zero speed) (c) s=(130−50)/(25−15)=80/10=8s = (130-50)/(25-15) = 80/10 = 8 m/s (d) Average speed = total distance / total time = 130/25=5.2130/25 = 5.2 m/s

7. Measuring Speed

Method 1: Ruler and Stopwatch

  1. Measure the distance with a ruler or tape measure
  2. Time the journey with a stopwatch
  3. Calculate speed = distance / time

Limitation: Human reaction time (~0.2 s) makes this inaccurate for fast objects or short times.

Method 2: Light Gates

  1. A card of known length passes through a light gate
  2. The light gate measures the time the card takes to pass
  3. Speed = card length / time

Advantage: Very accurate — no human reaction time error.

8. Practice Questions

    1. Calculate the speed of a car that travels 2400 m in 80 seconds. (2 marks)
    1. A cheetah runs at 30 m/s. How far does it travel in 12 seconds? (2 marks)
    1. Convert 108 km/h to m/s. (1 mark)
    1. A jogger runs 2 km in 10 minutes, then walks 1 km in 15 minutes. Calculate the average speed for the whole journey in m/s. (3 marks)
    1. Describe the motion shown by a distance-time graph that starts with a steep straight line, then becomes a horizontal line, then becomes a shallow straight line. (3 marks)

    Answers

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Frequently Asked Questions

What's the difference between speed and velocity?

Speed is a scalar (magnitude only). Velocity is a vector (magnitude and direction). A car doing 30 m/s has a speed. A car doing 30 m/s north has a velocity.

Can average speed be zero?

No, if any distance has been covered, average speed is positive. However, average velocity can be zero if you return to your starting point.

How do I find speed from a curved distance-time graph?

Draw a tangent line at the point of interest and calculate the gradient of that tangent. This gives the instantaneous speed.

Summary

  • Speed = distance ÷ time: s=d/ts = d/t
  • Speed is a scalar; velocity is a vector
  • Average speed = total distance ÷ total time
  • On a distance-time graph: gradient = speed
  • Horizontal line = stationary; steeper line = faster
  • Curved line = changing speed (acceleration/deceleration)
  • For curves: draw a tangent to find instantaneous speed
Tags:
#gcse#physics#forces#speed#distance#time#motion

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