Motion, Acceleration, and 1D Kinematics

Teacher Excellence WorkshopJune 18, 2008

Kinematic Quantities

What four quantities describe motion, and what are their SI units? Displacement (m) Velocity (m/s) Acceleration (m/s2) Time (s)

Unit conversion

Use the “railroad track” approach.

Kinematic Equations for uniformly accelerating

objects

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

Uniformly Accelerating Objects

• You see the car move faster and faster as time elapses.

• For each successive t, x is bigger.

• The velocity vs time graph reflects the increasing velocity.

What are the signs of velocity and acceleration? How is speed changing?

• This object is moving with positive velocity and acceleration. Speed is increasing.

• This object is moving with negative velocity and acceleration. Speed is increasing.

• This object is moving with negative velocity and positive acceleration. Speed is decreasing.

Draw Graphs forStationary Particles

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Draw Graphs forStationary Particles

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Draw Graphs forConstant Non-zero Velocity

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Draw Graphs forConstant Non-zero Velocity

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Draw Graphs for ConstantNon-zero Acceleration

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Draw Graphs for ConstantNon-zero Acceleration

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Practice Problem: A plane is flying in a northwest direction when it lands, touching the end of the runway with a speed of 130 m/s. If the runway is 1.0 km long, what must the acceleration of the plane be if it is to stop while leaving ¼ of the runway remaining as a safety margin?

Practice Problem: A plane is flying in a northwest direction when it lands, touching the end of the runway with a speed of 130 m/s. If the runway is 1.0 km long, what must the acceleration of the plane be if it is to stop while leaving ¼ of the runway remaining as a safety margin?

Practice Problem: What must a particular Olympic sprinter’s acceleration be if he is able to attain his maximum speed in ½ of a second?

Practice Problem: What must a particular Olympic sprinter’s acceleration be if he is able to attain his maximum speed in ½ of a second?

Practice Problem: On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from 0 to 20 m/s in 1.0 second.

a) What is the average acceleration of the passengers on this ride?

b) How fast would they be going if they accelerated for an additional second at this rate?

Practice Problem: On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from 0 to 20 m/s in 1.0 second.

a) What is the average acceleration of the passengers on this ride?

b) How fast would they be going if they accelerated for an additional second at this rate?

Practice Problem -- continued

c) Sketch approximate x-vs-t, v-vs-t and a-vs-t graphs for this ride.

Practice Problem -- continued

c) Sketch approximate x-vs-t, v-vs-t and a-vs-t graphs for this ride.

Practice Problem: Air bags are designed to deploy in 10 ms. Estimate the acceleration of the front surface of the bag as it expands. Express your answer in terms of the acceleration of gravity g.

Practice Problem: Air bags are designed to deploy in 10 ms. Estimate the acceleration of the front surface of the bag as it expands. Express your answer in terms of the acceleration of gravity g.

Practice Problem: You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and decelerate at 3.5 m/s2.a) How far do you travel before stopping?

b) When you have traveled only half the stopping distance, what is your speed?

Practice Problem: You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and decelerate at 3.5 m/s2.a) How far do you travel before stopping?

b) When you have traveled only half the stopping distance, what is your speed?

Practice Problem -- continuedc) How long does it take you to stop?

d) Draw x vs t, v vs t, and a vs t graphs for this.

Practice Problem -- continuedc) How long does it take you to stop?

d) Draw x vs t, v vs t, and a vs t graphs for this.

Free Fall

• Free fall is a term we use to indicate that an object is falling under the influence of gravity, with gravity being the only force on the object. Air resistance is considered negligible.

• Gravity accelerates the object toward the earth the entire time it rises, and the entire time it falls.

• Freefall is like any other type of accelerated motion; it’s just that the acceleration is pretty well defined. The acceleration due to gravity near the surface of the earth has a magnitude of 9.8 m/s2. The direction of this acceleration is DOWN.

Practice Problem: You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible,

a) how long is the ball in the air?

b) what is the ball’s speed and velocity when it strikes the ground at the base of the cliff?

c) sketch approximate x-vs-t, v-vs-t, a-vs-t graphs for this situation.

Practice Problem: You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible,

a) how long is the ball in the air?

b) what is the ball’s speed and velocity when it strikes the ground at the base of the cliff?

c) sketch approximate x-vs-t, v-vs-t, a-vs-t graphs for this situation.

Symmetry in Free Fall

• When something is thrown straight upward under the influence of gravity, and then returns to the thrower, this is very symmetric.

• The object spends half its time traveling up; half traveling down.

• Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with.

• Acceleration is 9.8 m/s2 and directed DOWN the entire time the object is in the air!

Practice Problem: You throw a ball straight upward into the air with a velocity of 20.0 m/s, and you catch the ball some time later.a) How long is the ball in the air?

b) How high does the ball go?

Practice Problem: You throw a ball straight upward into the air with a velocity of 20.0 m/s, and you catch the ball some time later.a) How long is the ball in the air?

b) How high does the ball go?

Practice Problem -- continuedc) What is the ball’s velocity when you catch it?

d) Sketch approximate x-vs-t, v-vs-t, a-vs-t graphs for this situation.

Practice Problem -- continuedc) What is the ball’s velocity when you catch it?

d) Sketch approximate x-vs-t, v-vs-t, a-vs-t graphs for this situation.

Reflex Testing

• Who’s got the quickest reflexes in the physics class? We’re dying to know.

• Using only a meter stick, test the reflexes of each person in your group by dropping the meter stick between his or her thumb and forefinger. One trial only per person, please!

• The quickest people from each lab table will participate in a “drop-off” at the end of class.

• We will then calculate the reaction time of the meter stick champion!

Sample problem: Bill drops a meter stick vertically through Ted’s thumb and forefinger, and Ted catches it as soon as he sees it fall. Ted’s thumb was originally at the 30 cm mark. When he catches the meter stick, his thumb is at the 53 cm mark. What is Bill’s reaction time?

Sample problem: Bill drops a meter stick vertically through Ted’s thumb and forefinger, and Ted catches it as soon as he sees it fall. Ted’s thumb was originally at the 30 cm mark. When he catches the meter stick, his thumb is at the 53 cm mark. What is Bill’s reaction time?

Sprinter Lab Preparation

• For the sprinter demonstrations, we will need:– 1 or more sprinters– 1 starter– 10 timers with stopwatches– 10 recorders with note cards and pens– a number of observers

• The timers with stopwatches will be arranged at 10 meter intervals. The starter and sprinter will be stationed at the starting point.

Sprinter Demonstration Procedure

• The timers will reset their stopwatches.• The starter will count down and start the race by

saying “go”. When he or she shouts “go”, the timers will start their stopwatches, and the sprinter will take off.

• As the sprinter passes each timer, the timer will stop the stopwatch. The recorder will record the time.

• We will do a few sprints, and then return to the classroom to begin data analysis.

A typical sprinter curve

A typical sprinter curve

A typical sprinter curve

A typical sprinter curve

Ode to an AP Physics Exam

You are hard and mean and bad,

But I will not let you make me sad!

I know the grading will be curvy,

So I’ll be brave and strong and nervy.

And if my grade doesn’t make me proud,

Exam grade repair is definitely allowed.

So, Physics Exam, prepare to meet your fate.

To master your secrets, I can hardly wait!