SPEED, VELOCITY AND ACCELERATION

• Scalars are quantities that are fully described by a magnitude (or numerical value) alone.• EXAMPLE: SPEED, TEMPERATURE, DISTANCE

• Vectors are quantities that are fully described by both a magnitude and a direction.• EXAMPLE: VELOCITY, ACCELERATION,

DISPLACEMENT

•Mass and Weight?

WHAT IS SPEED?

•Scalar quantity•Speed is the rate at which an Object/individaul covers distance.

• Calculate speed through this formula:

• Instantaneous Speed • Average Speed • You might think of the instantaneous speed as the speed that the speedometer reads at any given instant in time

and the average speed as the average of all the speedometer readings during the course of the trip. 

WHAT IS VELOCITY?

• Vector quantity• Velocity is the rate at which an object is

travelling plus the direction of the travel.• Use (+) positive or (-) negative sign to

designate direction. • + 10 m/s, - 10 m/s

• Average Velocity = distance move in a particular direction

time taken

WHAT IS ACCELERATION?

• Vector quantity• Acceleration is the change in velocity per unit of time.

• Acceleration= change in velocity = m/s² time taken

• Deceleration, or negative acceleration, is observed when an object slows down. The units are the same as for acceleration but the number has a negative symbol before it.

• Recognizing Acceleration:• Speeding up• Slowing down• Change direction

SAMPLE EXERCISES

• A car travels 500 m in 20 seconds. What is its average speed?

d/t = 500 meters = 25 m/s 20 sec

SAMPLE EXERCISES

• A boy runs after a bus. The bus is travelling at an average speed of 5 m/s. The boy runs 25 m in 6 s. Will he be able to catch the

bus?

• The man’s average speed is 25 ÷ 6 = 4.2 m/s. So he will not catch a bus moving at 5 m/s.

SAMPLE EXERCISES

• A car decelerates in 5 s from 35 m/s to 25 m/s.

• Its velocity changes by 25 - 35 = -10 m/s. Therefore its acceleration is -10 ÷ 5 = -2 m/s2

FREE FALL

TRUE or FALSE:1. The elephant and the feather each have the same

force of gravity.2. The elephant has more mass, yet both elephant and

feather experience the same force of gravity.3. The elephant experiences a greater force of gravity,

yet both the elephant and the feather have the same mass.

4. On earth, all objects (whether an elephant or a feather) have the same force of gravity.

5. The elephant weighs more than the feather, yet they each have the same mass.

6. The elephant clearly has more mass than the feather, yet they each weigh the same.

7. The elephant clearly has more mass than the feather, yet the amount of gravity (force) is the same for each.

8. The elephant has the greatest acceleration, yet the amount of gravity is the same for each.

In the absence of air resistance, both the elephant and the feather are in a state of free-

fall. That is to say, the only force acting upon the two objects is the force of gravity. This force of

gravity is what causes both the elephant and the feather to accelerate downwards. The force of gravity experienced by an object is dependent

upon the mass of that object.

Mass refers to the amount of matter in an object. Clearly, the elephant has more

mass than the feather. Due to its greater mass, the elephant also experiences a

greater force of gravity. That is, the Earth is pulling downwards upon the elephant with more force than it pulls downward

upon the feather. Since weight is a measure of gravity's pull upon an object, it would also be appropriate to say that

the elephant weighs more than the feather.

A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall.

There are two important motion characteristics that are true of free-falling objects:

A. Free-falling objects do not encounter air resistance.

B. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s2 .

9.8 m/s2

This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is

known as the acceleration of gravity - the acceleration for any object moving under

the sole influence of gravity and is denoted by the symbol g.

The most familiar example of motion with constant acceleration is

that of a body falling towards the earth. The acceleration of a falling

body is called acceleration of body and

is often denoted by g.

If the speed and time for a free-falling object being dropped from a position of rest were tabulated, then one

would note the following pattern:

Time (s) Speed (m/s)

0 0

1 9.8

2 19.6

3 29.4

4 39.2

5 49.0

and so on …

Thus, the velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen.

The formula for determining the velocity of a falling object after a time of t seconds is

vf = g * t

where vf = final velocity

g = acceleration of gravity

SAMPLE PROBLEM 1Calculate how far will Humpty fall in 3 seconds.

Solution:vf = g * t

vf = (9.8 m/s2) x (3 s)

vf = 29.4 m/s

The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall.

This distance fallen after a time of t seconds is given by the formula:

d = 1/2 * g * t2

where d = distance

g = acceleration of gravity

SAMPLE PROBLEM 2

Calculate how far Gwen has fallenin the first 10 seconds. (in a no-air-resistance clock tower)

Solution: d = 1/2 * 9.8 m/s2 * 102

d = 1/2 * 9.8 m/s2 * 100 d = 490 m

RELATIVITY

Galileo's ship is moving at a constant speed to the left. The fish remains stationary relative to the Earth. Galileo drops a

ball at time t1 that hits the ground at time t2. The fish's position is displayed at both times.

Galileo starts conducting simple mechanical experiments. For our example, let's imagine that he is simply dropping a

ball from the top of the ship's cabin to the floor, noting where it lands.

If the ship were stationary at the dock, the ball would drop straight to the floor directly beneath where Galileo were

holding it.

He discovered that the ball would simply fall directly below where it's dropped, just as if the ship were

stationary. From Galileo's point of view in the ship's hull, there was no difference between a ship with

constant velocity and a stationary one.But differences arise when you consider other

reference frames. In the drawing above, the front of the ship passes a stationary (relative to the Earth) fish at a specific time called t1. Seconds later at time t2, the ball

hits the floor of the ship as the middle of the ship passes over the fish.

Galileo formulated the principle of relativity in order to show that one cannot determine whether the earth revolves around

the sun or the sun revolves around the earth. The principle of relativity states that there

is no physical way to differentiate between a body moving at a constant speed and an immobile body. It is of course possible to

determine that one body is moving relative to the other, but it is impossible to determine

which of them is moving and which is immobile.

This means that there is no "absolute" velocity. Velocity measurements will differ depending upon the reference

frame in which they are measured. For instance, Galileo's ball had no horizontal velocity from his reference frame in the windowless ship. The fish, however, would see the ball having a horizontal velocity equal to that of the entire ship

floating overhead.

Neither measurement is "correct." Quite simply, it's all relative!

GALILEO AND THE SCIENTIFIC METHOD

GALILEO AND THE LEANING TOWER OF PISA

• Heavy and light objects fall at the same rate

• In a vacuum all bodies, regardless of their weight, shape, or specific gravity, are uniformly accelerated in exactly the same way.

INCLINED PLANE EXPERIMENT• Galileo could not observe the object's free

falling motion and at the time, technology was unable to record such high speeds. • Using a water clock, Galileo measured the time

it took for the ball to roll a known distance down the inclined plane. After many trials, he concluded that the total distance traveled by the object is proportional to the time squared needed for that travel.

GALILEO GALILEI• Father of experimental

science• Proved his hypothesis by

means of repeated scientific measurement; thus arriving at conclusions that led to mathematical relationships between measurable quantities. • His conclusions about

motion quantities are still applicable to all motion experiments and verifiable with the use of more accurate timers.

• “See now the power of truth; the same experiment which at first glance seemed to show one thing, when more carefully examined, assures us of the contrary.”

- Galileo Galilei

REFERENCES

• www.physicsclassroom.com• www.physicscentral.com• Introduction to College Physics and Chemistry