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38You have an initial velocity of -3.0 m/s. You then experience an acceleration of 2.5 m/s2 for 9.0s; what is your final velocity?

What is constant speed?If the speed of an object does not change, the object is traveling at a constant speed

ACCELERATION

Return toTable ofContentsAccelerationAccelerationAcceleration is the rate of change of velocity. a = vta = v - votacceleration = change of velocityelapsed timeAccelerationAcceleration is a vector, although in one-dimensional motion we only need the sign.

Since only constant acceleration will be considered in this course, there is no need to differentiate between average and instantaneous acceleration.a = v - votUnits for AccelerationUnits for acceleration

You can derive the units by substituting the correct units into the right hand side of these equations.= m/ssm/s2a = vt26Acceleration is the rate of change of _________ .AdisplacementBdistanceCspeedDvelocityanswerD

27The unit for velocity is:AmBm/sCm/s2Dft/s2answerB

28The metric unit for acceleration is:AmBm/sCm/s2Dft/s2answerC

29A horse gallops with a constant acceleration of 3m/s2. Which statement below is true?AThe horse's velocity doesn't change.BThe horse moves 3m every second.CThe horse's velocity increases 3m every second.DThe horse's velocity increases 3m/s every second.answerD

Solving ProblemsAfter you read the problem carefully:

1. Draw a diagram (include coordinate axes).

2. List the given information.

3. Identify the unknown (what is the question asking?)

4. Choose a formula (or formulas to combine)

5. Rearrange the equations to isolate the unknown variable.

6. Substitute the values and solve!

7. Check your work. (You can do the same operations to the units to check your work ... try it!)30Your velocity changes from 60 m/s to the right to 100 m/s to the right in 20 s; what is your average acceleration?answera = v/ta = (100-60)/20a = 2 m/s2

31Your velocity changes from 60 m/s to the right to 20 m/s to the right in 20 s; what is your average acceleration?answera = v/ta = (20-60)/20a = -2 m/s2

32Your velocity changes from 50 m/s to the left to 10 m/s to the right in 15 s; what is your average acceleration?answera = v/ta = (10-50)/15a = -4 m/s2

33Your velocity changes from 90 m/s to the right to 20 m/s to the right in 5.0 s; what is your average acceleration?answera = v/ta = (20-90)/ 5a = -14 m/s2

CHANGE in ???? ACTIVITY

Use a ramp and tennis ballMeasure distance/time on1st 1/2 rampMeasure distance/time on 2nd 1/2 ramp

What was the speed at each interval- What do you call this change?ACCELERATIONBUT-What exactly is acceleration?

Have the trucks in the animation move at the same speed but different acceleration. Which truck wins.

AccelerationAcceleration- rate of change in velocityOccurs when speed or direction changesNegative acceleration- when something slows downPositive acceleration- when something speeds upAn object with a zero acceleration always move at the same speed. Change in velocity / change in time = accelerationUnits m/s2 Meters per second per second

19Velocity- Time Graph20Velocity- Time graphSlope = accelerationFlat slope = constant speedPositive slope = speeding upNegative slope = slowing down21QuizReturn toTable ofContentsKinematics Equation 1a = vtMotion at Constant Accelerationbut since "" means change

v = v - vo and

t = t - to if we always let to = 0, t = t

Solving for "v"

This equation tells us how an object's velocity changes as a function of time.a = v - votat = v - vo

v - vo = at

v = vo + at35Starting from rest, you accelerate at 4.0 m/s2 for 6.0s. What is your final velocity?

36Starting from rest, you accelerate at 8.0 m/s2 for 9.0s. What is your final velocity?

37You have an initial velocity of 5.0 m/s. You then experience an acceleration of -1.5 m/s2 for 4.0s; what is your final velocity?

39How much time does it take to accelerate from an initial velocity of 20m/s to a final velocity of 100m/s if your acceleration is 1.5 m/s2?

40How much time does it take to come to rest if your initial velocity is 5.0 m/s and your acceleration is -2.0 m/s2?

41An object accelerates at a rate of 3 m/s2 for 6 s until it reaches a velocity of 20 m/s. What was its initial velocity?

42An object accelerates at a rate of 1.5 m/s2 for 4 s until it reaches a velocity of 10 m/s. What was its initial velocity?

In physics there is another approach in addition to algebraic which is called graphical analysis. The formula v = v0 + at can be interpreted by the graph. We just need to recall our memory from math classes where we already saw a similar formula y = mx + b.

From these two formulas we can some analogies:

v y (depended variable of x),v0 b (intersection with vertical axis),t x (independent variable), a m ( slope of the graph- the ratio between rise and run y/x). Graphing Motion at Constant Acceleration

Motion at Constant AccelerationBelow we can find the geometric explanation to the acceleration a =v/t which is the same a the slope of a given graph. 43The velocity as a function of time is presented by the graph. What is the acceleration?

44The velocity as a function of time is presented by the graph. Find the acceleration.

The acceleration graph as a function of time can be used to find the velocity of a moving object. When the acceleration is constant it can be shown on the graph as a straight horizontal line.

Motion at Constant Acceleration

In order to find the change is velocity for a certain limit of time we need to calculate the area under the acceleration line that is limited by the time interval. Motion at Constant Acceleration

The change in velocity during first 12 seconds is equivalent to the shadowed area

(4 x 12 = 48).

The change in velocity during first 12 seconds is 48 m/s. 45The following graph shows acceleration as a function of time of a moving object. What is the change in velocity during first 10 seconds?

CPO packet acceleration and speed time graphs#1-4Return toTable ofContentsFree Fall: Acceleration Due to GravityFree Fall

All unsupported objects fall towards the earth with the same acceleration. We call this acceleration the "acceleration due to gravity" and it is denoted by g.

g = 9.8 m/s2

Keep in mind, ALL objects accelerate towards the earth at the same rate.

g is a constant!It speeds up(negative acceleration)g = -9.8 m/s2It stops momentarily.v = 0g = -9.8 m/s2An object is thrown upward with initial velocity, voIt slows down.(negative acceleration)g = -9.8 m/s2What happens when it goes up?What happens when it goes down?What happens at the top?It returns with itsoriginal velocity.What happens when it lands?It speeds up.(negative acceleration)g = -9.8 m/s2It stops momentarily.v = 0g = -9.8 m/s2An object is thrown upward with initial velocity, voIt slows down.(negative acceleration)g = -9.8 m/s2It returns with itsoriginal velocity.av0On the way up:av1v1av2v2aavaav0On the way down:v1v1v2v2vvt = 0 st = 1 st = 2 st = 3 st = 0 st = 1 st = 2 st = 3 sv(m/s)t (s)An object is thrown upward with initial velocity, voIt stops momentarily.v = 0g = -9.8 m/s2It returns with itsoriginal velocity but in the opposite direction.For any object thrown straight up into the air, this is what the velocity vs time graph looks like.46A ball is dropped from rest and falls (do not consider air resistance). Which is true about its motion?Aacceleration is constantBvelocity is constantCvelocity is decreasingDacceleration is decreasing

cccc47An acorn falls from an oak tree. You note that it takes 2.5 seconds to hit the ground. How fast was it going when it hit the ground?

48A rock falls off a cliff and hits the ground 5 seconds later. What velocity did it hit the ground with?

49A ball is thrown down off a bridge with a velocity of 5 m/s. What is its velocity 2 seconds later?

50An arrow is fired into the air and it reaches its highest point 3 seconds later. What was its velocity when it was fired?

51A rocket is fired straight up from the ground. It returns to the ground 10 seconds later. What was it's launch speed?

Acceleration of a Bungee JumpNow take what you have just learned and contemplate a question about acceleration in the Veritasium video below:Click here for the videoMotion at Constant AccelerationIf velocity is changing at a constant rate, the average velocity is just the average of the initial and final velocities.And we learned earlier that xtv = v = v + vo2Some problems can be solved most easily by using these two equations together.xt= v + vo2xt= (v + vo)252Starting from rest you accelerate to 20 m/s in 4.0s. What is your average velocity?

53Starting with a velocity of 12 m/s you accelerate to 48 m/s in 6.0s. What is your average velocity?

54Starting with a velocity of 12 m/s you accelerate to 48 m/s in 6.0s. Using your previous answer, how far did you travel in that 6.0s?Previous Answeraverage velocity = 30 m/s

Return toTable ofContentsKinematics Equation 2Motion at Constant AccelerationWe can combine these three equations to derive an equation which will directly tell us the position of an object as a function of time.xtv = v = v + vo2xtv =x - xo = (v + vo)t x - xo = vt + vot x = xo + vot + vt x = xo + vot + (vo + at)t x = xo + vot + vot + at2x = xo + vot + at2

vot + at2D=v = vo + atXdKinematics equation 2 d=vot + at2

Motion at Constant AccelerationGraphical Approachv(m/s)t (s)A = lwIf the area under the graph is length x width (A = lw), then:

A = v0t Since we know that v = ,then area is really x.

A = x = v0tx tMotion at Constant AccelerationGraphical Approachv(m/s)t (s)A = bhIf the area under this graph is base x height, then:

A = t vSince we know that a = ,v = at.

A = x = t(at) = at2v tMotion at Constant AccelerationGraphical Approachv(m/s)t (s)Therefore, the area under a velocity vs. time graph is displacement. It can be calculated by combining the previous two results.

A = x = v0t + at2

x - x0 = v0t + at2

x = x0 + v0t + at2

d=vot + at2

at2v0tCPO PACKET-#5-755An airplane starts from rest and accelerates at a constant rate of 3.0 m/s2 for 30.0 s before leaving the ground. How far did it move along the runway?

56A Volkswagen Beetle moves at an initial velocity of 12 m/s. It coasts up a hill with a constant acceleration of 1.6 m/s2. How far has it traveled after 6.0 seconds?

57A motorcycle starts out from a stop sign and accelerates at a constant rate of 20 m/s2. How long will it take the motorcycle to go 300 meters?

58A train pulling out of Grand Central Station accelerates from rest at a constant rate. It covers 800 meters in 20 seconds. What is its rate of acceleration?

59A car has a initial velocity of 45 m/s. It accelerates for 4.8 seconds. In this time, the car covers 264 meters. What is its rate of acceleration?

60 A Greyhound bus traveling at a constant velocity starts to accelerate at a constant 2.0 m/s2. If the bus travels 500 meters in 20 seconds, what was its initial velocity?

Summary Kinematics is the description of how objects move with respect to a defined reference frame.

Displacement is the change in position of an object.

Average speed is the distance traveled divided by the time it took; average velocity is the displacement divided by the time. Instantaneous velocity is the limit as the time becomes infinitesimally short.

Average acceleration is the change in velocity divided by the time.

Instantaneous acceleration is the limit as the time interval becomes infinitesimally small.Summary (continued)

[Home > Position, Velocity, and Acceleration]

Learn about Position, Velocity, and Acceleration If you want to understand how an object (like a car, ball, person, or rocket) moves, you have to understand three things about what it means "to be moving." These three things "stick" to any object that moves, and are numbers that scientifically describe just how an object's motion is working. These three things are: Position. This is precisely where an object is located.

Speed. Precisely how fast an object is moving. and..(the most difficult for most people)...

Acceleration. Precisely how fast an object's speed is changing.

This selection allows you to play with the position, velocity, and acceleration for two objects at the same time. Try to learn about these three motion properties by comparing differences in your two objects' motion, for differently selected properties.

I'd like my first object to be a Big Red TruckSport Utility VehicleMotorcycleScooter

.

Start it at position 1 m5 m10 m15 m20 m

Give it a speed of 0 meters/second2.5 meters/second5 meters/second8 meters/second10 meters/second

Give it an acceleration of 0 meters/second*second1 meters/second*second2 meters/second*second4 meters/second*second6 meters/second*second10 meters/second*second-1 meters/second*second-2 meters/second*second-4 meters/second*second

I'd like my second object to be a Big Red TruckSport Utility VehicleMotorcycleScooter

.

Start it at position 1 m5 m10 m15 m20 m

Give it a speed of 0 meters/second2.5 meters/second5 meters/second8 meters/second10 meters/second

Give it an acceleration of 0 meters/second*second1 meters/second*second2 meters/second*second4 meters/second*second6 meters/second*second10 meters/second*second-1 meters/second*second-2 meters/second*second-4 meters/second*second

Notes: Negative accelerations try to get the objects to move towards the left, positive accelerations towards the right.

You must give an object either a velocity that is not zero, or an acceleration that is not zero (or both!), or it will not move at all!

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