Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Linked equations: s = vt, a = Δv/t
Notes
Distance–time graphs
- The gradient (slope) = speed.
- Horizontal line = stationary. Straight sloping line = constant speed. Steeper = faster.
- Curving upwards = accelerating; curving to flat = decelerating.
- (HT) If the line is curved, find the speed at one moment by drawing a tangent and measuring its gradient.
Velocity–time graphs
- The gradient = acceleration. A negative gradient = deceleration.
- Horizontal line = constant velocity (not stationary!).
- (HT) The area under the graph = distance travelled (split it into rectangles and triangles, or count squares).
Typical speeds
Walking ≈ 1.5 m/s | running ≈ 3 m/s | cycling ≈ 6 m/s | cars 13–30 m/s | sound in air ≈ 330 m/s. An object falling freely near the Earth’s surface accelerates at about 9.8 m/s².
Questions
Q1 (F) What does a horizontal line on a distance–time graph show?
Show answer
The object is stationary – its distance isn’t changing.
Q2 (F) A distance–time graph is a straight line from (0 s, 0 m) to (20 s, 100 m). Calculate the speed.
Show answer
Speed = gradient = 100 ÷ 20 = 5 m/s
Q3 (F) What does a horizontal line on a velocity–time graph show?
Show answer
The object is moving at a constant velocity (zero acceleration).
Q4 (F) Give the typical speed of a person walking.
Show answer
About 1.5 m/s.
Q5 (F/H) A velocity–time graph goes in a straight line from 0 m/s to 12 m/s in 4 s. Calculate the acceleration.
Show answer
Acceleration = gradient = (12 − 0) ÷ 4 = 3 m/s²
Q6 (F/H) What does a line sloping downwards on a velocity–time graph show?
Show answer
The object is decelerating (slowing down) – the gradient is negative.
Q7 (H) A car accelerates steadily from rest to 10 m/s in 5 s, then travels at 10 m/s for 10 s. Use the area under the velocity–time graph to find the total distance travelled.
Show answer
Triangle: ½ × 5 × 10 = 25 m
Rectangle: 10 × 10 = 100 m
Total = 125 m
Q8 (H) A distance–time graph is curved. How do you find the speed at a particular time?
Show answer
Draw a tangent to the curve at that time, then calculate the gradient of the tangent (change in distance ÷ change in time). That gradient is the speed at that moment.
