Class 1 - Motion in One Dimension • Introduction • Average Velocity • Instantaneous Velocity • Acceleration • Homework 1
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Class 1 - Motion in One Dimension
• Introduction
• Average Velocity
• Instantaneous Velocity
• Acceleration
• Homework
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Average Velocity
Consider the motion of the car shown in the figure below.
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Average Velocity (cont’d)
The graph of this motion is shown below.
The average velocity is defined as the distance traveled divided
by elapsed time
vx = ∆x
∆t =
xf − xi
tf − ti
where ∆x = xf −
xi is called the displacement.
The average velocity is the slope of the line joining the initial
and final points on the position-time graph.
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Example 1: Calculating Average Velocity
From the position versus time graph for the motion of the car,
estimate the average velocity of the car between (a) points A
and B and (b) points C and E.
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Example 1 Solution
From the position versus time graph for the motion of the car,
estimate the average velocity of the car between (a) points A
and B and (b) points C and E.
(a) vx = ∆x∆t
= xf −xi
tf −ti= 55m−30m
10s−0 = 2.5m/s
(b) vx = ∆x
∆t =
xf −xi
tf −ti = −37m−37m
40s−20s = −
3.7m/s
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Example 2
You drive your BMW down a straight road for 5.2 km at 43
km/h, at which point you run out of gas. You walk 1.2 km
farther, to the nearest gas station, in 27 min. (a) Calculate your
total displacement. (b) Calculate the total elapsed time. (c)
What is your average velocity from the time you started your
car to the time you arrived at the gas station?
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Example 2 Solution
You drive your BMW down a straight road for 5.2 km at 43
km/h, at which point you run out of gas. You walk 1.2 km
farther, to the nearest gas station, in 27 min. (a) Calculate your
total displacement. (b) Calculate the total elapsed time. (c)
What is your average velocity from the time you started your
car to the time you arrived at the gas station?
(a) ∆x = 5.2km + 1.2km = 6.4km
(b) ∆t = 5.2km43km/h
+ 27min = 0.12h + 0.45h = 0.57h
(c) vx = ∆x
∆t
= 6.4km
0.57h
= 11km/h
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Graphical Representation of InstantaneousVelocity
The instantaneous velocity at a particular instant in time is the
slope of the position versus time graph at that instant.
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Example 3
Estimate the instantaneous velocity of the car at point D in the
position versus time graph below.
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Example 3 Solution
Estimate the instantaneous velocity of the car at point D in the
position versus time graph below.
vx = ∆x∆t
= −40m−40m40s−20s
= −4.0m/s
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Example 4
The position of a particle moving along the x-axis is given by
x(t) = 7.8 + 9.2t − 2.1t3
with x in meters and t in seconds. What is the velocity of the
particle at t = 3.5 s?
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Example 4 Solution
The position of a particle moving along the x-axis is given by
x(t) = 7.8 + 9.2t − 2.1t3
with x in meters and t in seconds. What is the velocity of the
particle at t = 3.5 s?
vx(t) = dx(t)dt = 9.2 − 6.3t2
vx(t = 3.5s) = 9.2 − 6.3(3.5)2 = −68m/s
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Example 5
(a) Your car, starting from rest, gets up to 55 km/h in 3.2 s.
What is its average acceleration?
(b) Later, you brake your car to rest from 55 km/h in 4.7 s.What is its average acceleration in this case?
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