# Unit 3, Uniform Acceleration Notes - Mr. B's Honors Physics

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Unit 3, Uniform Acceleration Notes

Notes 𝑿v 𝒕1. Find the instantaneousvelocity at t 2.0 s and t 8.0sby finding slopes of tangents.To find the slope of the tangent I 0,25will find the slope of the secantslines where the mid-times are 2and 8s. 𝒗a 𝒕4,216, 162. Determine the averageacceleration from t 2.0s to t 8.0s V change in the instantaneousvelocity (not the average velocity).2810, 0

Physics Bell Work, Wednesday, Sept 30Δt 1s2. Draw a motion map for the runner shown aboveshowing that velocity is not constant but acceleration isuniform .v vaavvaaavvvaa

Physics Bell Work, Wednesday, Sept303. How are motion maps in questions 1 & 2 different?Map 1 is constant velocity (arrows same length, same dotspacing.

Physics Bell Work, Monday, Feb 20t (s)0.024.06.08.010.0x (m)4.010.016.022.028.034.04.Worksheet3, question24. Plot the data (draw thegraph)5. Calculate the slope6. 𝟑𝟒Determinethe𝒎velocity.𝒎 𝟒𝒎5. 𝟑𝟏𝟎 𝒔𝒔6. Slope of an x-t graph velocity, 3 m/s𝒙𝒇 𝒙𝒊𝒕𝒇 𝒕𝒊(s)v

Bell Work Wednesday, 10/3/181. On a motion map how do we show an object is speedingWe must add an acceleration vector to the motionup or slowing down?map.2. Draw velocityand acceleration vectors that show anobject that is speeding up and then slowing down to a stopat uniform acceleration.Object speedingupObject slowingdown to a stop.vava When the object’s acceleration vectors are in the samedirection as its velocity vectors, the object is speedingup. When the vectors are in opposite directions, the objectis slowing down.

1. A ball rolling up a ramp and the reversing direction androlling down the ramp. Draw the motion map, velocity-timeand acceleration-time graph that describes this motion.vav v (m/s) -a (m/s2)a0Time (s)-

Velocity with Average AccelerationIf an object’s average acceleration during a time intervalis known, then it can be used to determine how much thevelocity changed during that time.The definition of average acceleration:can be rewritten as follows:

Velocity with Average AccelerationThe equation for final velocity with averageacceleration can be written as follows:The final velocity is equal to the initial velocityplus the product of the average acceleration andtime interval.

Velocity with Average AccelerationIn cases in which the acceleration is constant, theaverage acceleration, ā, is the same as theinstantaneous acceleration, a. The equation forfinal velocity can be rewritten to find the time atwhich an object with constant acceleration has agiven velocity.It also can be used to calculate the initial velocityof an object when both the velocity and the time atwhich it occurred are given.

Position with Constant AccelerationOn the graph shown on theright, v is the height of theplotted line above the t-axis,while Δt is the width of theshaded rectangle. The area ofthe rectangle, then, is vΔt, orΔd. Thus, the area under thev-t graph is equal to theobject’s displacement.

Position with Constant AccelerationThe area under thev-t graph is equal to theobject’s displacement.

Finding the Displacement from av-t GraphThe v-t graph shows themotion of an airplane. Findthe displacement of theairplane at Δt 1.0 s andat Δt 2.0 s.

Finding the Displacement from av-t GraphAre the units correct?Displacement is measured in meters.Do the signs make sense?The positive sign agrees with the graph.Is the magnitude realistic?Moving a distance of about one football field in 2 sis reasonable for an airplane.

Section3.1 AccelerationDetermining Acceleration from a vt GraphThe following equation expresses averageacceleration as the slope of the velocity-timegraph.Average acceleration is equal to the change invelocity, divided by the time it takes to make thatchange.

Section3.1 Section CheckQuestion 1Which of the following statements correctly definesacceleration?A. Acceleration is the rate of change of displacement ofan object.B. Acceleration is the rate of change of velocity of anobject.C. Acceleration is the amount of distance covered inunit time.D. Acceleration is the rate of change of speed of anobject.

Section3.1 Section CheckAnswer 1Reason: The rate at which an object’s velocitychanges is called acceleration of theobject.

Section3.1 Section CheckQuestion 2What happens when the velocity vector and theacceleration vector of an object in motion are inthe same direction?A. The acceleration of the object increases.B. The speed of the object increases.C. The object comes to rest.D. The speed of the object decreases.

Section3.1 Section CheckAnswer 2Reason: When the velocity vector and theacceleration vector of an object inmotion are in the same direction, thespeed of the object increases.

Section3.1 Section CheckQuestion 3On the basis of thevelocity-time graph of acar moving up a hill, asshown on the right,determine the averageacceleration of the car?A. 0.5 m/s2C. 2 m/s2B. -0.5 m/s2D. -2 m/s2

Section3.1 Section CheckAnswer 3Reason: Average acceleration of an object isthe slope of the velocity-time graph.

Section3.2 Motion with Constant AccelerationVelocity with Average AccelerationIf an object’s average acceleration during a time intervalis known, then it can be used to determine how much thevelocity changed during that time.The definition of average acceleration:can be rewritten as follows:

Section3.2 Motion with Constant AccelerationVelocity with Average AccelerationThe equation for final velocity with averageacceleration can be written as follows:The final velocity is equal to the initial velocityplus the product of the average acceleration andtime interval.

Section3.2 Motion with Constant AccelerationVelocity with Average AccelerationIn cases in which the acceleration is constant, theaverage acceleration, ā, is the same as theinstantaneous acceleration, a. The equation forfinal velocity can be rewritten to find the time atwhich an object with constant acceleration has agiven velocity.It also can be used to calculate the initial velocityof an object when both the velocity and the time atwhich it occurred are given.

Section3.2 Motion with Constant AccelerationPosition with Constant AccelerationThe position data atdifferent time intervalsfor a car with constantacceleration are shownin the table.The data from the tableare graphed as shownon the next slide.

Section3.2 Motion with Constant AccelerationPosition with Constant AccelerationThe graph shows that thecar’s motion is not uniform:the displacements for equaltime intervals on the graphget larger and larger.The slope of a position-timegraph of a car moving with aconstant acceleration getssteeper as time goes on.

Section3.2 Motion with Constant AccelerationPosition with Constant AccelerationThe slopes from the positiontime graph can be used tocreate a velocity-time graphas shown on the right.Note that the slopes shownin the position-time graphare the same as thevelocities graphed in thevelocity-time graph.

3.1 Which of the following statements correctly defines acceleration? Question 1 A. Acceleration is the rate of change of displacement of an object. B. Acceleration is the rate of change of velocity of an object. C. Acceleration is the amount of distance covered in unit time. D. Acceleration is the rate of change of speed of an object. Section .

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