SME
Grade 11 Science · Problem type
Braking distance
Use this for “A car at 25 m/s brakes at 5 m/s² to a stop. How far does it go, and how long does it take?”
Chart
v = v₀ + at = 25 + (−5) × 4
v = 5 m/s
Δx
=
v₀ + v
2
×
t
=
25 + 5
2
×
4
Δx = 60 m
The shaded area above the axis is the displacement (+).
This is an example. Type your own values to start a new problem.
(
v (m/s)
)
2
=
(
v₀ (m/s)
)
2
+
2
×
(
a (m/s²)
)
×
Δx (m)
t
Time
calculated
Formulas
v
2
=
v₀
2
+
2
×
a
×
Δx
5
2
=
25
2
+
2
×
(−5)
×
60
v
=
v₀
+
a
×
t
5 = 25 + (−5) × 4
Assumptions
•
The brakes give a steady acceleration against the motion: a < 0.
•
v² = v₀² + 2aΔx needs no time: use it when the time is not given.
•
A stop is v = 0.
Step-by-step
WE KNOW
v₀ = 25 m/s, v = 5 m/s, a = −5 m/s²
FIND
displacement (Δx), time (t)
Step 1 · Find displacement (Δx)
Use v² = v₀² + 2 × a × Δx
The
change
in
the
square
of
the
speed,
over
2
a
.
Δx
=
(
v
2
−
v₀
2
)/(2
×
a
)
Δx
=
(
5
2
−
25
2
)/(2
×
(−5))
Δx = (25 − 625)/(−10)
Δx = −600/(−10)
Δx = 60 m
Step 2 · Find time (t)
Use v = v₀ + a × t
Divide the change in velocity by the change each second.
t
=
(
v
−
v₀
)/
a
t
=
(5
−
25)/(−5)
t
=
−20/(−5)
t
=
4
s
Check
Put the numbers back in. Both sides should match.
5
2
=
25
2
+
2
×
(−5)
×
60
✓
5 = 25 − 5 × 4 ✓
Topic check
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