Accelerated Motion

Acceleration

Acceleration: the rate at which velocity changes

Acceleration =

• Unit:

time velocityΔ

time

velocityoriginal - velocityfinal

2sm

sm/s

time velocityΔ

Remember, velocity is how fast (speed) AND in what direction.

If either speed OR direction changes, the velocity has changed, which means that there is an acceleration!

Constant velocity means that neither the speed nor the direction of motion can change.

A race car driving around a circular path at a constant 80 mi/h has a constant speed but not a constant velocity since its direction is changing.

An object accelerates when its speed OR its direction changes!

So……

How to tell if you accelerated too quickly from a red light.

Positive or Negative?Choose a direction for + and – then stick

with it!

Going forward, speeding up

Going forward, slowing down

Going backward, speeding up

Going backward, slowing down

Positive positive

positive negative

negativenegative

negativepositive

Velocity Acceleration

KEY WORDS

“stops” The final velocity is zero, vf = 0

“at rest” The original velocity is zero, vo = 0

d (meters) = displacement- the change in your position

vO (meters / second) = original velocity

vf (meters / second) = final velocity

t (seconds) = time

a (m/s2) = acceleration

The Kinematics EquationsAre used to analyze accelerated motion

Free Fall

Do heavier things fall faster than lighter things?

AristotleGreek philosopher,

b. 384 B.C.

It’s OBVIOUS that heavy things fall faster than lighter things.

Every object has its own “natural” rate of falling

Learning what to IGNORE is sometimes as important as

learning what to pay attention to.

What will we ignore (mostly)?

Galileo…Galileo found that,

ignoring the effect of the air, all freely falling objects had the SAME acceleration, regardless of their mass or the height from which they were dropped.

The Law of Falling Bodies

Born in Pisa 1564

Free Fall: the movement of an object in response to a gravitational attraction

Earth’s gravity, ignoring air resistance, produces an acceleration of we often just call “g”, the acceleration due to gravity.

The size of “g” is 9.8 m/s2, but since the acceleration is always downward, the value of the acceleration is

a = - g = - 9.8 m/s2

(approximately -10 m/s2)

What does this mean?Each second of free-fall, the speed of

an object increases by about 10 m/s

T = 1s

Speed = 10 m/s

T = 2s

Speed = 20 m/s

T = 3s

Speed = 30 m/s

Positive or Negative?Up= positive

Down = NegativeIf you throw a ball upward,As it moves upward, its

velocity is positive.As it falls back down, its

velocity is negative.At the highest position, its

velocity isZERO.

What about the sign of acceleration?On the way up, its acceleration is

negative.

On the way down, its acceleration is negative.

At the highest point, its acceleration is negative.

The acceleration is ALWAYS negative!

It’s always -9.8 m/s2 because the acceleration is due to CONSTANT gravity!

What’s the

speed?

30 m/s

20 m/s

10 m/s

0 m/s

10 m/s

20 m/s

30 m/s

If the ball was thrown upward with a velocity of 50 m/s, how long would it take to reach its highest point?

What if the original velocity was 70 m/s? 35 m/s?

Does the ball travel the same distance during each second?

MORE KEY WORDS“dropped”: vo = 0, a = -9.8 m/s2 (-10 m/s2)

“reaches its highest point”: velocity = 0

In ALL free fall problems, the acceleration

a = - 9.8 m/s2

Remember, you need to find THREE numbers to be able to solve for the fourth quantity.

Once the basket ball player’s feet leave the ground, what is his ONLY acceleration?

- 9.8 m/s2

Remember, “how fast” is NOT the same as

“how far”

A bird egg falls out of a nest high in a tree.

How FAST is it moving in 1 second?

Vo = 0 a = -10 m/s2 t = 1s vf = ?

Vf = -10 m/s

Remember, “how fast” is NOT the same as “how far”

A bird egg falls out of a nest high in a tree.

How FAR will it fall in 1 second?

d = vot + ½ at2

d = 0 + ½ (-10) 12

d = -5 m

Why is “d” a negative value?