GCSE Physics - How to Solve: Speed, Distance, Time, and Acceleration Calculations

How to Solve: Speed, Distance, Time, and Acceleration Calculations

Complete Guide (GCSE/A-Level Physics, Chemistry, Biology – Exam-Ready!)

Introduction

"Mastering speed, distance, time, and acceleration calculations unlocks 10–15% of your GCSE Physics paper—and real-world problems like predicting car braking distances, rocket launches, or even how fast a virus spreads in a population. One wrong unit or formula, and you lose easy marks. Let’s fix that."

WHAT YOU NEED TO KNOW FIRST

1. Units: You must know how to convert between km/h, m/s, and other units (e.g., 1 m/s = 3.6 km/h).
2. Rearranging equations: You should be able to solve for any variable in an equation (e.g., distance = speed × time → time = distance ÷ speed).
3. Graphs: Understand how to read distance-time and speed-time graphs (slope = speed/acceleration).

KEY TERMS & FORMULAS

Key Terms

Formulas

(All must be memorised unless marked "given on exam sheet.")

1. Speed, Distance, Time [ \text{speed} = \frac{\text{distance}}{\text{time}} \quad \text{or} \quad v = \frac{s}{t} ]
2. v = speed (m/s or km/h)
3. s = distance (m or km)

4. t = time (s or h) MEMORISE THIS

5. Acceleration [ \text{acceleration} = \frac{\text{change in velocity}}{\text{time}} \quad \text{or} \quad a = \frac{v - u}{t} ]

6. a = acceleration (m/s²)
7. v = final velocity (m/s)
8. u = initial velocity (m/s)

9. t = time (s) MEMORISE THIS

10. Uniform Acceleration (SUVAT Equations) (Given on exam sheet, but practice using them!)

11. ( v = u + at )
12. ( s = ut + \frac{1}{2}at^2 )
13. ( v^2 = u^2 + 2as )
14. ( s = \frac{(u + v)}{2} \times t )

STEP-BY-STEP METHOD

(Follow these steps for EVERY problem.)

1. Read the question carefully.
2. Underline key numbers and units.

3. Circle what you’re asked to find (e.g., "Find the acceleration").

4. List known values.

5. Write down every given number with its unit (e.g., u = 5 m/s, t = 10 s).

6. Check units.

7. Convert all units to match the formula (e.g., km/h → m/s by ÷3.6).

8. Pick the right formula.

9. Use the formula that includes the variable you need to find.

10. Rearrange the formula (if needed).

11. Example: If you need time but have speed and distance, rearrange ( v = \frac{s}{t} ) to ( t = \frac{s}{v} ).

12. Plug in the numbers.

13. Substitute values into the formula.

14. Calculate and add units.

15. Write the answer with the correct unit (e.g., 12 m/s²).

16. Check your answer.

17. Does it make sense? (e.g., A car accelerating at 50 m/s² is unrealistic—probably wrong!)

Worked Example Using the Steps

Question: A cyclist travels 150 m in 30 s. What is their speed?

1. Read: Find speed. Given: distance = 150 m, time = 30 s.
2. Known values: s = 150 m, t = 30 s.
3. Units: Already in m and s—no conversion needed.
4. Formula: ( v = \frac{s}{t} ).
5. Rearrange: Not needed.
6. Plug in: ( v = \frac{150}{30} ).
7. Calculate: ( v = 5 ) m/s.
8. Check: 5 m/s is reasonable for a cyclist.

Answer: 5 m/s.

WORKED EXAMPLES

Example 1 – Basic (Speed)

Question: A car travels 240 km in 3 hours. What is its speed in km/h?

1. Known: s = 240 km, t = 3 h.
2. Formula: ( v = \frac{s}{t} ).
3. Plug in: ( v = \frac{240}{3} ).
4. Calculate: ( v = 80 ) km/h.

What we did and why: Used the basic speed formula because we had distance and time. No unit conversion was needed.

Example 2 – Medium (Acceleration)

Question: A train accelerates from 10 m/s to 30 m/s in 5 s. What is its acceleration?

1. Known: u = 10 m/s, v = 30 m/s, t = 5 s.
2. Formula: ( a = \frac{v - u}{t} ).
3. Plug in: ( a = \frac{30 - 10}{5} ).
4. Calculate: ( a = \frac{20}{5} = 4 ) m/s².

What we did and why: Used the acceleration formula because we had initial/final velocity and time. No unit conversion was needed.

Example 3 – Exam-Style (Disguised Problem)

Question: A rocket’s velocity increases from 50 m/s to 200 m/s in 10 s. How far does it travel during this time?

1. Read: Find distance (s). Given: u = 50 m/s, v = 200 m/s, t = 10 s.
2. Known: Need s, but we don’t have a yet.
3. Step 1: Find a first.
4. ( a = \frac{v - u}{t} = \frac{200 - 50}{10} = 15 ) m/s².
5. Step 2: Now use SUVAT to find s.
6. Formula: ( s = ut + \frac{1}{2}at^2 ).
7. Plug in: ( s = (50 \times 10) + \frac{1}{2} \times 15 \times 10^2 ).
8. Calculate: ( s = 500 + 750 = 1250 ) m.

What we did and why: The question didn’t give acceleration directly, so we had to calculate it first. Then we used the SUVAT equation for distance.

COMMON MISTAKES

1. MISTAKE: Forgetting units.
2. Why it happens: Rushing or not writing units in working.

3. Correct approach: Always write units next to numbers (e.g., 5 m/s, not just 5).

4. MISTAKE: Mixing up speed and velocity.

5. Why it happens: Not reading the question carefully (e.g., "displacement" vs. "distance").

6. Correct approach: If the question mentions direction, use velocity/displacement. Otherwise, use speed/distance.

7. MISTAKE: Using the wrong formula.

8. Why it happens: Not listing known/unknown variables first.

9. Correct approach: Write down what you know and what you need to find before picking a formula.

10. MISTAKE: Not converting units.

11. Why it happens: Assuming all units match (e.g., km/h vs. m/s).

12. Correct approach: Convert everything to base units (m, s, m/s) before calculating.

13. MISTAKE: Ignoring negative acceleration.

14. Why it happens: Forgetting that deceleration is negative acceleration.
15. Correct approach: If an object slows down, a is negative.

EXAM TRAPS

1. TRAP: "Average speed" vs. "instantaneous speed."
2. How to spot it: The question asks for average speed over a journey with stops.

3. How to avoid it: Use total distance ÷ total time, not just one segment.

4. TRAP: Graph questions with hidden acceleration.

5. How to spot it: A speed-time graph with a curved line (non-uniform acceleration).

6. How to avoid it: For curved lines, use the area under the graph for distance, not just slope.

7. TRAP: Missing the "change in velocity" in acceleration.

8. How to spot it: The question gives final and initial velocity but asks for acceleration.
9. How to avoid it: Always use ( a = \frac{v - u}{t} ), not just ( \frac{v}{t} ).

1-MINUTE RECAP

"Here’s what you need to remember tonight:
1. Speed = distance ÷ time. Memorise it. Rearrange it if you need time or distance.
2. Acceleration = change in velocity ÷ time. If an object slows down, acceleration is negative.
3. Units matter. Convert km/h to m/s by ÷3.6. Always write units in your answer.
4. For SUVAT problems: List u, v, a, s, t, pick the right equation, and solve step by step.
5. Watch for traps: Average speed, negative acceleration, and graph questions will try to trick you. Read carefully!

Now go practice 3 problems. You’ve got this!"