GED Science
Motion, Speed & Acceleration
Speed is how fast position changes: distance divided by time. Acceleration is how fast SPEED changes — speeding up, slowing down, or turning all count. The test lives on the d = rt triangle and on reading motion graphs.
The words first
- speed
- distance ÷ time (mph, m/s)
- velocity
- speed plus a direction
- acceleration
- any change in speed or direction over time
- constant speed
- speed not changing — zero acceleration, even if moving fast
The method
THE TRIANGLE d = r × t
d cover what you want:
───── want r? r = d ÷ t
r │ t want t? t = d ÷ r
want d? d = r × t
UNITS MUST MATCH: minutes with minutes, hours with hours.
30 minutes = 0.5 hour before it touches an mph problem.
READING A DISTANCE-TIME GRAPH
straight rising line → constant speed (steeper = faster)
flat line → stopped
curving steeper → accelerating
ACCELERATION IN NUMBERS
change in speed ÷ time taken
0 to 60 mph in 6 s → 60 ÷ 6 = 10 mph per second
Worked all the way through
The problem
A bus travels 150 miles in 2.5 hours. What is its average speed?
- Step 1 — Pick the triangle piece you want.You want the rate: r = d ÷ t.
- Step 2 — Check the units agree.Miles and hours — already matched for mph.
- Step 3 — Divide.150 ÷ 2.5 = 60.
- Step 4 — Attach units.60 miles per hour, on average — it may have gone faster and slower along the way.
On the board
r = d ÷ t
cover the r
r = 150 ÷ 2.5
r = 60 mph
"average" — the whole trip smoothed out
Answer
60 mph
A second one, in a different form
A cyclist goes from 4 m/s to 10 m/s in 3 seconds. What is her acceleration?
change in speed: 10 − 4 = 6 m/s
time: 3 s
6 ÷ 3 = 2
2 m/s each second
her speed grows by 2 every second
Answer
2 m/s² — she gains 2 m/s of speed every second
The usual mistake
Using the final speed instead of the change when computing acceleration.
Check yourself
Write the triangle, cover the letter you want, and convert units BEFORE computing. A speed of 60 with mismatched units is worth zero points; the test plants a wrong answer for exactly that mistake.
Practice it
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