Graphical Analysis
Average speed = ∆x/∆t = (8 m)/(2 s) = 4 m/s
The slope of the curve is constant, so the speed is constant
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Changing speed
v2 = 0
v1 = (400 m)/(200 s) = 2 m/s
v3 = (–400 m)/(400 s) = –1 m/s
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Speed not constant
Instantaneous speed at t = 20 s is (26 m)/(5 s) = 5.2 m/s
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Acceleration
Acceleration = (12 m/s)/(2 s) = 6 m/s2
The slope of the curve is constant, so the acceleration is constant
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What are speeds, average acceleration?
2.58
x f inal − xinitial
Speed =
Time
Average acceleration =
vA =
10 − 40
= −20 km/h
1.5
vB =
20 − 10
= +10 km/h
2.5 − 1.5
vC =
40 − 20
= +40 km/h
3.0 − 2.5
vC − vA 40 − (−20)
=
= 20 km/h2
T
3
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2.61 What is the average acceleration?
Dv
vC − vA
ā =
=
t − t0
3.5 hrs
ā = −8.5 km/h2
25 − 0 km
= 25 km/h
1 hour
27 − 33 km
vC =
= −4.6 km/h
3.5 − 2.2 hours
vA =
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Speed, Velocity and Acceleration
Average speed =
Distance
x − x0
=
Elapsed time t − t0
Displacement
D!x
Average velocity =
=
Elapsed time t − t0
Instantaneous velocity !v = lim
Dt→0
D!x
Dt
change in velocity !v −!v0
Average acceleration =
=
elapsed time
t − t0
D!v
Instantaneous acceleration = lim
Dt→0 Dt
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