Physics · Grades 9–12

Motion & graphs · Quick reference

Reference sheet for Grades 9 to 12: describing motion from position data and reading motion graphs. Find how far the object moves in each second.

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Rule and key idea

Describing motion from position data

Find how far the object moves in each second. Equal steps mean constant speed; growing steps mean speeding up; shrinking steps mean slowing down.

equal distances in equal times → constant speed · average speed = total distance ÷ total time

A cart moves along a straight track. Its position is recorded every second: t = 0 s: 7 m; t = 1 s: 22 m; t = 2 s: 34 m; t = 3 s: 43 m; t = 4 s: 49 m. How is the cart moving? → It is slowing down.

Reading motion graphs

Always read the axis labels first: the same shape means different things on a position-time graph and on a velocity-time graph.

slope of position-time = velocity · slope of velocity-time = acceleration · area under velocity-time = displacement

On a velocity-time graph, the line is horizontal at 5 m/s. What is the object doing? → It moves at a constant velocity of 5 m/s.

Check yourself

Four practice questions on this topic. Try each one before you open the answer.

Signed velocity changes from 6 m/s to 7 m/s in 7 s. Find the average acceleration. Round to 3 decimal places if needed. Answer in m/s².
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0.143 m/s² a = (v₂ − v₁)/Δt (7 − 6) / 7 = 0.143
Signed velocity changes from 9 m/s to 39 m/s in 5 s. Find the average acceleration. Round to 3 decimal places if needed. Answer in m/s².
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6 m/s² a = (v₂ − v₁)/Δt (39 − 9) / 5 = 6
Which straight segment shows larger speed: slope +2 m/s or slope −5 m/s?
- The +2 m/s segment
- The −5 m/s segment
- Both have the same speed
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The −5 m/s segment Speed is the magnitude of velocity; 5 is greater than 2.
A robot moves 130 m east and then 27 m west along a straight line. Find the total distance travelled. Round to 3 decimal places if needed. Answer in m.
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157 m distance = forward path + return path 130 + 27 = 157