SME
Grade 8 Science · Problem type
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?”
Chart
Slope = rise ÷ run = 6 m/s ÷ 4 s = 1.5 m/s²
v = v₀ + a × t
= 2 m/s + 1.5 m/s² × 4 s = 8 m/s
d = (v₀ + v) ÷ 2 × t
= (2 m/s + 8 m/s) ÷ 2 × 4 s = 20 m
Evenly spaced dots mean a steady speed; spreading dots mean speeding up
This is an example. Type your own values to start a new problem.
v (m/s)
=
v₀ (m/s)
+
a (m/s²)
×
t (s)
d
Distance
worked out (not typed)
Formulas
v
=
v₀
+
a
×
t
(final
speed
=
starting
speed
+
acceleration
×
time)
8 = 2 + 1.5 × 4
d
=
(
v₀
+
v
)
÷
2
×
t
(distance
=
(starting
speed
+
final
speed)
÷
2
×
time)
20 = (2 + 8) ÷ 2 × 4
Assumptions
•
Acceleration is how much the speed changes each second, in m/s² (meters per second, per second).
•
On a speed-time graph the slope is the acceleration and the area under the line is the distance.
•
The dots above spread out as the cart speeds up.
Step-by-step
WE KNOW
v₀ = 2 m/s (starting speed), a = 1.5 m/s² (acceleration), t = 4 s (time)
FIND
final speed (v), distance (d)
Step 1 · Find final speed (v)
Use v = v₀ + a × t (final speed = starting speed + acceleration × time)
Start
at
v₀
and
add
a
for
every
second.
v
=
2
+
1.5
×
4
v
=
2
+
6
v
=
8
m/s
Step 2 · Find distance (d)
Use d = (v₀ + v) ÷ 2 × t (distance = (starting speed + final speed) ÷ 2 × time)
The area under the line: the average speed times the time.
d
=
2 + 8
2
×
4
d
=
10
2
×
4
d
=
5
×
4
d
=
20
m
Check
Put the numbers back in. Both sides should match.
8 = 2 + 1.5 × 4 ✓
20 = (2 + 8) ÷ 2 × 4 ✓
Topic check
See what you know: 5 questions on this topic
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Related lessons
Speed, velocity and acceleration
Main lesson
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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?”