A learner walks 9 m east, then 4 m west on one line. Find total distance.
Answer and explanation
13 m
Distance adds both path lengths: 9 + 4 = 13 m.
Subjects
Motion & graphs
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Sample exercises
For the same 9 m east and 4 m west trip, use east-positive. Find displacement.
Answer and explanation
5 m
Signed displacement is +9 − 4 = +5 m.
A runner returns to the start after one complete lap. Which is zero?
- Elapsed time necessarily
- Displacement
- Distance travelled
Answer and explanation
Displacement
Final and initial positions coincide, so displacement is zero.
On a signed axis, x changes from −6 m to +8 m. Find displacement.
Answer and explanation
14 m
Subtract initial from final: 8 − (−6) = 14 m.
Which quantity needs a direction or sign in one dimension?
- Elapsed time
- Displacement
- Distance
Answer and explanation
Displacement
Displacement is a vector quantity, represented by a sign on a one-dimensional axis.
Can two journeys have equal displacement and different distances? Give an example.
Answer and explanation
Yes. A direct 5 m trip and a 9 m forward, 4 m backward trip both end 5 m ahead.
Credit same endpoints and different path lengths.
Study notes
Distance is not displacement
Use paths and signed positions to explain round trips.
Grades 6–9Distance is not displacement · Revision sheet
Use paths and signed positions to explain round trips.
Grades 6–9Average speed and average velocity
Choose the correct numerator and include stops in elapsed time.
Grades 7–10Average speed and average velocity · Revision sheet
Choose the correct numerator and include stops in elapsed time.
Grades 7–10Reading position–time information
Interpret slopes without confusing the graph with a picture of a path.
Grades 7–10Reading position–time information · Revision sheet
Interpret slopes without confusing the graph with a picture of a path.
Grades 7–10Velocity–time graphs: slope and area
Separate acceleration from displacement when interpreting a graph.
Grades 9–12Velocity–time graphs: slope and area · Revision sheet
Separate acceleration from displacement when interpreting a graph.
Grades 9–12Circular motion: changing velocity at constant speed
Keep centripetal acceleration and actual force sources distinct.
Grades 10–12Circular motion: changing velocity at constant speed · Revision sheet
Keep centripetal acceleration and actual force sources distinct.
Grades 10–12Projectile components and model limits
Treat horizontal and vertical motion together without inventing horizontal gravity.
Grades 10–12Projectile components and model limits · Revision sheet
Treat horizontal and vertical motion together without inventing horizontal gravity.
Grades 10–12Average speed over two stages
Add all distances and all elapsed times before dividing.
Grades 6–9Displacement and average velocity
Use consistent SI units and keep the stated direction convention.
Grades 7–10Distance on a return journey
Distance adds path lengths; displacement uses the change in position.
Grades 6–9Acceleration from two readings
Use consistent SI units and keep the stated direction convention.
Grades 8–11Velocity with constant acceleration
This equation requires constant acceleration over the interval.
Grades 9–12Displacement with constant acceleration
Displacement may be negative; do not automatically take its absolute value.
Grades 9–12Idealized stopping time
b is the positive magnitude of constant deceleration; reaction time is excluded.
Grades 9–12Idealized braking distance
Assume straight-line motion and constant deceleration up to rest.
Grades 10–12Closing speed
Add speeds only here because the objects move directly toward each other.
Grades 8–11Time to maximum height
At the highest point velocity is zero, but gravitational acceleration is not.
Grades 10–12Free fall from rest
Treat g as constant, ignore air resistance, and start from rest.
Grades 9–12Horizontal projectile range
Initial vertical velocity is zero; ignore air resistance and use level ground below.
Grades 10–12Motion & graphs · Formula reference 1
Formula reference
Grades 6–12Motion & graphs · Formula reference 2
Formula reference
Grades 8–12Motion & graphs · Formula reference 3
Formula reference
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