How to Solve: Speed, Velocity, Acceleration

How to Solve: Speed, Velocity, Acceleration

Hook (10 seconds on camera): "If you can’t tell the difference between speed and velocity, you’ll lose half the marks on motion questions—let’s fix that in 10 minutes."

What You Need To Know First

1. Distance vs. Displacement – Distance is how far you travel (scalar). Displacement is how far you are from the start and in which direction (vector).
2. Units – Meters (m), seconds (s), meters per second (m/s), meters per second squared (m/s²).
3. Graphs – You should be able to read distance-time and velocity-time graphs.

Key Vocabulary

Formulas To Know

Step-by-Step Method

Step 1: Read the question carefully.

• Underline numbers, units, and keywords (e.g., "starts from rest," "comes to a stop," "north," "uniform acceleration").
• Decide if the question is about speed, velocity, or acceleration.

Step 2: Identify what you’re solving for.

• Are you finding speed, velocity, acceleration, distance, or time?
• Write down the unknown variable (e.g., a = ?).

Step 3: List the given values.

• Write down every number from the question with its unit and symbol.
• Example:
• Initial velocity (u) = 0 m/s (starts from rest)
• Final velocity (v) = 20 m/s
• Time (t) = 4 s

Step 4: Choose the right formula.

• If the question is about speed, use v = d/t.
• If it’s about velocity, use v = s/t (displacement, not distance).
• If it’s about acceleration, use a = Δv/t or v = u + at.

Step 5: Plug in the numbers and solve.

• Substitute the values into the formula.
• Show every step (examiners give marks for working).
• Include units in every calculation.

Step 6: Check your answer.

• Does the unit make sense? (e.g., m/s for speed, m/s² for acceleration).
• Does the number make sense? (e.g., a car can’t accelerate at 1000 m/s²).
• If the question asks for direction, include it (e.g., "5 m/s east").

Worked Examples

Example 1 – Basic (Speed)

Question: A runner covers 400 meters in 50 seconds. What is her speed?

Step 1: Underline key info. - Distance (d) = 400 m - Time (t) = 50 s - Find: Speed (v)

Step 2: Choose formula. - v = d/t

Step 3: Plug in numbers. - v = 400 m / 50 s

Step 4: Solve. - v = 8 m/s

Step 5: Check. - Unit: m/s ✔️ - Number: 8 m/s is reasonable for a runner ✔️

Answer: 8 m/s

What we did and why: We used the speed formula because the question gave distance (not displacement) and asked for speed (not velocity). No direction was needed.

Example 2 – Medium (Velocity & Acceleration)

Question: A car starts from rest and reaches 30 m/s in 6 seconds. What is its acceleration?

Step 1: Underline key info. - Initial velocity (u) = 0 m/s (starts from rest) - Final velocity (v) = 30 m/s - Time (t) = 6 s - Find: Acceleration (a)

Step 2: Choose formula. - a = Δv / t or a = (v – u) / t

Step 3: Plug in numbers. - a = (30 m/s – 0 m/s) / 6 s

Step 4: Solve. - a = 30 m/s / 6 s = 5 m/s²

Step 5: Check. - Unit: m/s² ✔️ - Number: 5 m/s² is reasonable for a car ✔️

Answer: 5 m/s²

What we did and why: We used the acceleration formula because the question gave initial and final velocities and asked for acceleration. Since the car starts from rest, u = 0.

Example 3 – Exam Style (Disguised Problem)

Question: A cyclist moves 100 m east in 10 s, then 50 m west in 5 s. What is her average velocity?

Step 1: Underline key info. - First part: 100 m east in 10 s - Second part: 50 m west in 5 s - Find: Average velocity

Step 2: Understand the difference. - Speed = total distance / total time - Velocity = displacement / total time

Step 3: Calculate displacement. - East = +100 m - West = -50 m - Total displacement = +100 m – 50 m = 50 m east

Step 4: Calculate total time. - 10 s + 5 s = 15 s

Step 5: Use velocity formula. - v = displacement / time - v = 50 m / 15 s ≈ 3.33 m/s east

Step 6: Check. - Unit: m/s ✔️ - Direction: Must include "east" (velocity is a vector) ✔️

Answer: 3.33 m/s east

What we did and why: We calculated displacement (not distance) because velocity depends on direction. The cyclist ended up 50 m east of the start, so that’s the displacement.

Common Mistakes

Exam Traps

1-Minute Recap

"Okay, let’s lock this in. Speed is just how fast you’re going—no direction. Velocity is speed plus direction. Acceleration is how fast your velocity changes, and it can be positive (speeding up) or negative (slowing down).

Formulas to memorize: - Speed = distance / time - Velocity = displacement / time - Acceleration = change in velocity / time

Biggest traps? 1. Mixing up distance and displacement—if the question mentions direction, it’s velocity. 2. Forgetting that "comes to rest" means final velocity = 0. 3. Not checking units—always write them in your answer.

Pro tip: If you’re stuck, write down every number from the question with its symbol. Then pick the formula that fits.

You’ve got this. Now go ace that exam!