motion in one dimensionsection 2 what do you think? which of the following cars is accelerating?...

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?


Preview

• Objectives

• Changes in Velocity

• Motion with Constant Acceleration

• Sample Problem

Chapter 2 Section 2 Acceleration


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.


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)


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


Velocity and Acceleration


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

+ +

+ -

- -

- +


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


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


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


Equations for Constantly Accelerated Straight-Line Motion



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


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?


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



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 .




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


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?


Velocity vs. Time Graphs

Constant speed



+ Acceleration



Deceleration or negative acceleration



Yellow line represents faster

acceleration



Constant speed of 30 m/s



Red line represents faster rate of deceleration (3 m/s2

) .



Red line represents faster acceleration than green, blue

line represents deceleration or negative acceleration.

motion in one dimensionsection 2 what do you think? which of the following cars is accelerating?...

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