Motion in One Dimension Section 2
What do you think?
• Which of the following cars is accelerating?– A car shortly after a stoplight turns green– A car approaching a red light– A car with the cruise control set at 80 km/h– A car turning a curve at a constant speed
• Based on your answers, what is your definition of acceleration?
Motion in One Dimension Section 2
Preview
• Objectives
• Changes in Velocity
• Motion with Constant Acceleration
• Sample Problem
Chapter 2 Section 2 Acceleration
Motion in One Dimension Section 2
Objectives
• Describe motion in terms of changing velocity.
• Compare graphical representations of accelerated and nonaccelerated motions.
• Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.
Motion in One Dimension Section 2
Acceleration
• Acceleration is the rate at which velocity changes over time. • What are the units?
– SI Units: (m/s)/s or m/s2
– Other Units: (km/h)/s or (mi/h)/s• An object accelerates if its speed, direction, or both change.• Acceleration has direction and magnitude. Thus, acceleration is a vector
quantity• Acceleration = 0 implies a constant velocity (or rest)
Motion in One Dimension Section 2
Classroom Practice Problem
• Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s.– Answer: 9.3 m/s2 downward
Motion in One Dimension Section 2
Velocity and Acceleration
Motion in One Dimension Section 2
Direction of Acceleration
Describe the motion of an object with
vi and a as shown to the left.
• Moving right as it speeds up
• Moving right as it slows down
• Moving left as it speeds up
• Moving left as it slows down
Vi a
+ +
+ -
- -
- +
Motion in One Dimension Section 2
Graphing Velocity
• The slope (rise/run) of a velocity/time graph is the acceleration.– Rise is change in v– Run is change in t
• This graph shows a constant acceleration.
• Average speed is the midpoint.
2i f
avg
v vv
Motion in One Dimension Section 2
Graph of v vs. t for a train
• Describe the motion at points A, B, and C.
• Answers– A: accelerating (increasing
velocity/slope) to the right– B: constant velocity to the
right– C: negative acceleration
(decreasing velocity/slope) and still moving to the right
Motion in One Dimension Section 2Chapter 2
Motion with Constant Acceleration
• When velocity changes by the same amount during each time interval, acceleration is constant.
• The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide. These equations apply to any object moving with constant acceleration.
• These equations use the following symbols:x = displacement
vi = initial velocity
vf = final velocityt = time interval
Section 2 Acceleration
Motion in One Dimension Section 2
Useful Equations
1.
2.
3.
4.
5.
2i f
avg
v vv
avg
xv
t
avg
va
t
f iv v a t
21
2ix v t a t
2 2 2f iv v a x
Motion in One Dimension Section 2Chapter 2
Equations for Constantly Accelerated Straight-Line Motion
Section 2 Acceleration
Motion in One Dimension Section 2
Classroom Practice Problems
• A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval?– Answer: 84 m
• An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing?– Answer: -18.0 m/s2
Motion in One Dimension Section 2
Sample Problem
Final Velocity After Any Displacement
A person pushing a stroller starts from rest, uniformly
accelerating at a rate of 0.500 m/s2. What is the
velocity of the stroller after it has traveled 4.75 m?
Motion in One Dimension Section 2
Sample Problem, continued
1. DefineGiven:
vi = 0 m/s a = 0.500 m/s2
x = 4.75 m
Unknown: vf = ?
Diagram: Choose a coordinate system. The most convenient one has an origin at the initial location of the stroller, as shown above. The positive direction is to the right.
Chapter 2 Section 2 Acceleration
Motion in One Dimension Section 2Chapter 2
Sample Problem, continued
2. PlanChoose an equation or situation: Because
the initial velocity, acceleration, and displacement are known, the final velocity can be found using the following equation:
2 2 2f iv v a x
2 2f iv v a x
Rearrange the equation to isolate the unknown: Take the square root of both sides to isolate vf .
Section 2 Acceleration
Motion in One Dimension Section 2
Sample Problem, continued
Tip: Think about the physical situation to determine whether to keep the positive or negative answer from the square root. In this case, the stroller starts from rest and ends with a speed of 2.18 m/s. An object that is speeding up and has a positive acceleration must have a positive velocity. So, the final velocity must be positive.
3. CalculateSubstitute the values into the equation and solve:
4. EvaluateThe stroller’s velocity after accelerating for 4.75 m is 2.18 m/s to the right.
2 2(0 m/s) 2(0.500 m/s )(4.75 m)fv
2.18 m/sfv
Motion in One Dimension Section 2
Now what do you think?
• Which of the following cars is accelerating?– A car shortly after a stoplight turns green– A car approaching a red light– A car with the cruise control set at 80 km/h– A car turning a curve at a constant speed
• Based on your answers, what is the definition of acceleration?• How is acceleration calculated?• What are the SI units for acceleration?
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Constant speed
Motion in One Dimension Section 2
Velocity vs. Time Graphs
+ Acceleration
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Deceleration or negative acceleration
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Yellow line represents faster
acceleration
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Constant speed of 30 m/s
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Red line represents faster rate of deceleration (3 m/s2
) .
Motion in One Dimension Section 2
Velocity vs. Time Graphs
Red line represents faster acceleration than green, blue
line represents deceleration or negative acceleration.