Speed, Velocity and Acceleration

Linear MotionChapter 2

Linear Motion

• Motion is easy to recognize but can be hard to describe

• The following quantities are used to describe motion: speed, velocity and acceleration

• Each of these is a rate. A rate is a quantity divided by time.

• Motion along a straight line is sometimes called linear motion.

All Motion is relative

• All motion is relative to a reference.• This means that we describe motion of an

object relative to some other object• In our environment, the reference for motion

is the earth’s surface, and speeds are measured relative to the earth

• The earth moves at 107,000 km/h relative to the sun

Speed

• Speed is a measure of how fast something is moving.• It is the rate at which a distance is covered• Units of speed could be: km/h, m/s, mi/h, ft/s• In physics we use units of m/s for speed

• s = d/t

s

d

ttime

distancespeed

Instantaneous Speed

• Instantaneous speed is speed at any instant in time.

• A speedometer measures speed in ‘real time’ (the instantaneous speed).

Average Speed• Average speed is the average of all

instantaneous speeds; found simply by a total distance/total time ratio

• The average speed of a trip:

• For more information http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L1d.html

timeelapsed

distance total speed average

Velocity and Speed• In physics we distinguish between speed and velocity:

• Speed refers to how quickly an object moves (a scalar quantity).

• Velocity is defined as speed in a given direction or rate of change of position (displacement over time). v = x/t

• Velocity refers to both the speed and direction of motion of an object (a vector quantity).

• Negative velocity means the object is moving in the opposite direction

• Motion at constant velocity means that both the speed and direction of an object do not change.

• In a car, we can change the velocity three ways: gas pedal to speed up, brake to slow down or steering wheel to change direction

Velocity Triangle

• Speed and velocity triangles are similar because v = x/t

• Find the equation for displacement, and time using the triangle

• x = v x t• t = x/v

v

x

t

Velocity Questions

1) How far does Bob run if he maintains an average velocity of 3 m/s for 10 s?

2) List three ways you can change the velocity of your car.

3) Is it possible to go around a corner without changing velocity? Explain.

4) One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.

Acceleration• For its velocity to change, an object must

accelerate.

• An object accelerates whenever its speed or direction or both change.

• Acceleration may be positive (increasing speed) or negative (decreasing speed).

• Acceleration is a measure of how quickly the velocity changes: a = v/t

interval time

velocityof changeonaccelerati

Acceleration at constant speed

• An object moving in a circle at constant speed is always accelerating (changing direction).

• http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/kinema/avd.html

• If you have starting and ending velocity or speed, find that before you use the triangle.

• If not, use triangle to find change in velocity (v), then find initial or final velocity

• v = ending velocity – starting velocity

Solving Acceleration Problems using Acceleration Triangle

a

v

t

More Acceleration Equations

• The equations x = v x t and d = s x t can only be used when the is no acceleration (velocity is constant)

• If there is an acceleration and the starting velocity is zero, the following equations must be used for distance or displacement: x = ½ at2 and d = ½ at2

• If there is an acceleration, and the starting velocity is zero, the following equation describes the velocity at any time: v = a x t or v = at

• Note: If the starting velocity is not zero we use the equations: v = v0 + at and x = v0t + ½ at2 but student in this class will not be required to use these equations

Acceleration Questions

1) A dragster going at 15 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration?

2) The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 10 m/s in a time of 2 seconds. Find his acceleration.

3) Find the acceleration of a car that travels at a constant velocity of 45 Km/hr for 10 s.

4) Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5 m/s2.

Free fall, an example of acceleration

• Free fall is when an object is falling being affected only by gravity. That means NO air resistance.

Free Fall – All objects fall at the same rate

• If you drop a coin and a feather at the same time you will notice that the coin reaches the ground way before the feather.

• However, if you were to take the air out of the container you would find that the coin and feather fall together and hit the bottom at the same time!

Acceleration due to gravity, g• Newton told us that every object with mass attracts every other

object with mass and the size of the attraction depends on the mass of each object and the distance between the objects

• We don’t feel the attraction of most objects because their mass is small relative to the Earth which has a huge mass.

• The Earth pulls so that objects experience an acceleration of about 10 m/s2. This acceleration is given a special letter, g.

• g = 10 m/s2 This number is important, remember it!• So during each second an object is in free fall, its velocity

increases by 10 m/s. If the object experiences air resistance its velocity won’t increase as fast because air resistance will slow it down.

Challenge Question

• Suppose someone throws a ball straight upward with a speed of 30 m/s and at the same time throws one straight down with a speed of 30 m/s. Which ball will be traveling faster when it hits the ground, the one thrown straight upward or the one thrown straight down? Assume there is no air resistance.

Time and velocity for an object in free fall v = gt

g

v

t

Time and Distance for an object in free fall d = ½ gt2

g

dt

2

Free Fall Questions – How Fast?

1) When a ball is thrown straight down, by how much does speed increase each second on Earth?

2) When a ball is thrown straight up, by how much does speed decrease each second?

3) In free fall, do a feather and a ball fall side by side? Explain.4) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s.5) Suppose a rock is dropped on a planet where the acceleration due to

gravity it 5 m/s2, by how much would the speed change each second?6) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the

end of the 3 s interval?7) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after

6s of free fall.

Free Fall Questions – How Far?1) For a freely falling rock does the distance fallen each second stay the

same, increase with time, or decrease with time?2) A ball is dropped from rest and freely falls for 6 s. How many meters has it

fallen in 6 s?3) A ball is thrown straight upward and travels 5 m until it reaches the top of

its path.a) How far will it fall before it reaches its initial position?b) How long will it take to fall that distance?c) How long will the ball be in the air?

4) A ball is thrown straight up and returns to Earth 6 s later.a) Find its speed at the top of its path.b) Find its acceleration at the top its path.c) How long does it take to reach the top of its path?d) How fast is it traveling when it returns to Earth?e) Challenge: What is its maximum height?

Additional Free Fall Review

1) If one had only a stopwatch, could one determine the initial speed of a ball launched vertically upward from the earth’s surface? Explain.

2) With only a stopwatch, could one determine how high the ball travels before it stops? Explain.

Motion Graphs – Position vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graphs – Velocity vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graph Questions

1) What do you think might be happening in this graph?

2) What do you think position and velocity graphs of free fall motion might look like? Try to sketch them.

Sources

• http://rigel.physics.unr.edu/faculty/phaneuf/classinfo/index100.html

• Conceptual Physics by Paul Hewitt• Hs-staffserver.stjames.k12.mn.us/~schisa/

PowerPoint/Physics/3Chapter2.ppt