Accelerated Motion

Changing motion

• You can feel the difference between uniform and nonuniform motion

• When motion changes, you feel a push or pull (a force).– Ex: a Marta train coming to a sudden stop

• In uniform motion, your body becomes used to it.– Ex: sitting in a car on cruise control

Acceleration

• Whenever we change our state of motion, we are accelerating.

• Acceleration is how quickly we are changing our velocity

• Acceleration: the rate at which velocity is changing– SI unit: m/s2 or meters per second per

second– Ex: speeding up, slowing down (negative

acceleration), changing direction

Check Your Understanding

If a dog chases its tail in a circle at the same speed the whole time, is it accelerating?

Yes! Even though its speed is staying constant, it is changing direction, and therefore changing its velocity. If the velocity changes, it is accelerating.

– Equation: a = Δv / t = (vf – vi) / t• a = acceleration (m/s2)• Δv = change in velocity (m/s)• vf = final velocity (m/s)

• vi = initial velocity (m/s)

• t = time (s)

Check Your Understanding

Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration?

We see that the speed increases by 5 km/h each second. The acceleration

would be 5 km/h.s during each interval.

In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. What is the acceleration of each vehicle?

a = Δv / tacar = ? atruck = ?

Δvcar=65–50=15 km/h Δvtruck=15-0=15 km/ht = 5s t = 5s

acar = (15 km/h) / (5s) atruck = (15 km/h) / (5s)

acar = 3 km/h.s atruck = 3 km/h.s

Check Your Understanding

Which undergoes a greater acceleration?

Although the speeds are different, their rate of change of speed is the same…so both have the same acceleration.

Check Your Understanding

Elapsed time: the time that has passed since the beginning of a fall– How long it takes something to fall– SI unit: seconds

Elapsed Time

Free Fall

• Consider an apple falling from a tree. We know that it starts at rest and gains speed as it falls, or accelerates.

• Gravity causes the apple to accelerate downward and is said to be in free fall.

Free fall: when an object is only affected by gravity – SI unit: m/s2 ( for acceleration due to gravity) – Ex: ag = 10 m/s2 on Earth.

• The letter ag represents the acceleration due to gravity.

–Equation: v = ag t• v = velocity or speed (m/s)• ag = acceleration due to gravity (~10 m/s2

on Earth)• t = elapsed time (s)

**Hint - as soon as you see any of the following phrases in a word problem, write g = 10 m/s2 for a given: free fall, falling, dropped, thrown**

Check Your UnderstandingWhat would the speedometer reading on

a falling rock be 4.5 seconds after it drops from rest?

v = ?

ag = 10 m/s2

t = 4.5s

v = ag t

v = (10 m/s2) (4.5s)

v = 45 m/s

How about 8 seconds? v = ?

ag = 10 m/s2

t = 8sv = gt

v = (10 m/s2) (8s)v = 80 m/s

How about 15 seconds? v = ?

ag = 10 m/s2

t = 15sv = gt

v = (10 m/s2) (15s)v = 150 m/s

• Now consider an object thrown straight up. It will continue to move straight up, then it comes back down.

• At the highest point, the object changes its direction and the objects instantaneous speed is 0 m/s.

• Whether the object is moving up or down, the acceleration of the object is always 10 m/s2.

• Because an object in free fall increases the rate of distance covered every second, we cannot use v =d/t.

–Equation: d = ½ ag t2

• d = distance (m)• ag = acceleration due to gravity (10 m/s2 on

Earth)• t = elapsed time (s)

Check Your Understanding

What is the distance an object falls in one second?

d = ?ag = 10 m/s2

t = 1 s

d = ½ ag t2

d = ½ (10)(12)d = 5 m

Air Resistance and Free Fall

• All objects fall at ~10 m/s2 on Earth• Regardless of weight or mass• Ex: In a vacuum, a feather and a bowling ball will hit

the ground at the same time if dropped from the same hieght• A vacuum is anyway without any air (ex: outer space)

• Air resistance causes objects such as a coin and a feather to accelerate differently. • However, air resistance less noticeably affects the

motion of more massive objects like stones and baseballs.

• With negligible air resistance, falling objects can be considered to be in free fall.

Velocity – Time Graphs

• Velocity-Time graphs show the change of velocity over an elapsed time– AKA Speed-Time

graphs• Remember that speed

does NOT take into account direction

• Time is always the independent variable

• Velocity is always the dependent variable

0

10

20

30

40

50

60

0 10 20 30 40 50

• The slope of a Velocity-Time graph is equal to acceleration

• Slope = rise/run• Slope = change in velocity / time

– a = Δv / t– The steeper the slope, the faster the acceleration

• Remember acceleration can be speeding up, slowing down, or sharp turns

– A positive slope is speeding up and moving forward– A negative slope is EITHER slowing down OR moving

backwards– A zero slope means that the velocity is NOT

changing, meaning that the object is moving at the same speed in the same direction

Check Your Understanding

Which person(s) could be slowing down?

Person C. They have a negative slope; they could be moving backwards too (there is not enough info on the graph to tell).

Check Your Understanding

Which person(s) are not accelerating?

A and E. Their have a constant velocity.

Which person(s) could be speeding up?

B and D. They are increasing velocity each second.