SME
Grade 8 Science · Physical Science
Speed, velocity and acceleration
Use this for “A cart moves at 3 m/s for 4 s. How far does it go?” and its speed from a distance and a time.
Chart
Slope = rise ÷ run = 12 m ÷ 4 s = 3 m/s
d = v × t = 3 m/s × 4 s = 12 m
The steeper the line, the faster it goes
This is an example. Type your own values to start a new problem.
d (m)
=
v (m/s)
×
t (s)
Formulas
d
=
v
×
t
(distance
=
speed
×
time)
12 = 3 × 4
Assumptions
•
Speed is the distance covered each second, in meters per second (m/s). 1 m/s is 3.6 km/h, about 2.2 mi/h.
•
On a distance-time graph a steady speed is a straight line; the steeper, the faster. A flat line is standing still.
•
Velocity is speed with a direction: 3 m/s east. Walking back toward the start is a negative velocity.
•
The dots above the graph are the position each second: evenly spaced at a steady speed.
Step-by-step
WE KNOW
v = 3 m/s (speed), t = 4 s (time)
FIND
distance (d)
Step 1 · Find distance (d)
Use d = v × t (distance = speed × time)
Each
second
covers
v
meters:
multiply
by
the
seconds.
d
=
3
×
4
d
=
12
m
Check
Put the numbers back in. Both sides should match.
12 = 3 × 4 ✓
Topic check
See what you know: 5 questions on this topic
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More problem types
A walk on a position-time graph
Use this for “On a position-time graph, when is the walker standing still, moving fastest, or heading back to the start?”
Speeding up: a speed-time graph
Use this for “A cart speeds up from 2 m/s at 1.5 m/s² for 4 s. How fast is it going, and how far did it go?”
Steady, speeding up or slowing down?
Use this for “A toy car’s position is marked each second. Is it moving steadily, speeding up or slowing down?”