Notes on Motion IVAcceleration

a

Acceleration

What do you think of when someone says acceleration?

If you think speeding up – then you are almost completely correct!!!!

It turns out that an object is accelerating if it

Speeds up

Slows down

Or changes direction

Defining Acceleration

Acceleration is defined as the rate of change of velocity.

Another way to say this is that acceleration measures how fast an objects velocity changes.

Accelerations can be positive or negativeBut

Positive acceleration doesn’t always mean an object is speeding up.

Negative acceleration doesn’t always mean an object is slowing down.

Speeding Up or Slowing DownFor linear motion (straight-line). Whether or not an

object speeds up or slows down is determined by the direction of the acceleration COMPARED to

the direction of motion (velocity).

If an object is moving in the positive direction and its acceleration is also

positive, then the object will speed up.v

a

If an object is moving in the negative direction and its acceleration is also

negative, then the object will speed up.v

a

If an object is moving in the positive direction and its acceleration is also

negative, then the object will slow down.v

a

If an object is moving in the negative direction and its acceleration is also

positive, then the object will slow down.v

a

In general, if the acceleration and velocity have the same sign (both positive or both

negative), then the object:

SPEEDS UP

In general, if the acceleration and velocity have different signs (one positive and one negative),

then the object:

SLOWS DOWN

Units for AccelerationEnglish System

Feet per Second per Second (ft/s/s or ft/s2)

Metric SystemKilometers per Hour per second (km/hr/s),

Meters per Second per Second (m/s/s or m/s2))

In science the most common unit is:

m/s/s or m/s2

Meaning of AccelerationA car starts from rest and accelerates at 4 km/hr/s.

What does this mean?

This means the car’s velocity changes by 4 km/hr each second.

Starting Velocity:Velocity after 1-s:Velocity after 2-s:

Velocity after 10-s:

0 km/hr

4 km/hr

8 km/hr

40 km/hr

Meaning of AccelerationA car traveling at 10 km/hr accelerates at 4 km/hr/s.

What does this mean?

This means the car’s velocity changes by 4 km/hr each second.

Starting Velocity:Velocity after 1-s:Velocity after 2-s:

Velocity after 10-s:

10 km/hr

14 km/hr

18 km/hr

50 km/hr

Meaning of AccelerationA car traveling at 8 km/hr accelerates at-4 km/hr/s.

What does this mean?

This means the car’s velocity changes by -4 km/hr each second.

Starting Velocity:Velocity after 1-s:Velocity after 2-s:Velocity after 10-s:

8 km/hr

4 km/hr

0 km/hr

-32 km/hr

STOPPED!!!!!!

CHANGED DIRECTIONS

Solving Problems with AccelerationAcceleration is defined as the rate of change of

velocity. Since this is a rate of change we can also say that acceleration is the change in

velocity over time. As an equation this looks like:

vf is the final velocity (ending) and vi is the initial velocity (starting).

This will find the average acceleration if the change in velocity is over a time interval.

This will find the uniform acceleration if the acceleration is constant.

t

vva if

Solving Problems with Acceleration

If we place his formula into our triangle, we can find other useful formulas from this

vf - vi

a tt

vva if

Solving Problems with Velocity and Speed

a t

If you need to find t, cover t.Since vf - vi is on top of a, divide them.

t

vva if

vf - via

vvt if

Solving Problems with Velocity and Speed

a t

If you need to find vf, cover vf-vi.Since a is next to t, multiply them.

Finally add vi to both sides.

t

vva if

vf - vi

a

vvt if

atvv if atvv if

Solving Problems with Acceleration

vf - vi

a t

Example Problem 1:A car is travelling at 15-m/s when it begins to pass a slower car. The car accelerates to 20-m/s in 0.5-s. What is the car’s acceleration?

Know:vi = 15-m/svf = 20-m/st = 0.5-s

Find:

a = ?

Formula: Solve:

t

vva if

210

5.05

5.01520

sma

a

Solving Problems with Acceleration

vf - vi

a t

Example Problem 2:A car is traveling at 25-m/s when its brakes are applied slowing it to a stop. This takes 2.0-s. What is the acceleration of the car?

Know:vi = 25-m/svf = 0-m/st = 2.0-s

Find:

a = ?

Formula: Solve:

t

vva if

25.120.225

0.2250

sma

a

Solving Problems with Acceleration

vf - vi

a t

Example Problem 3:How long would it take a car starting from rest to reach a speed of 45-m/s if it accelerates at 5.0–m/s2?

Know:vi = 0-m/svf = 45-m/sa = 5.0–m/s2

Find:

t = ?

Formula: Solve:

a

vvt if

sa

t

90.545

0.5045

Solving Problems with Acceleration

vf - vi

a t

Example Problem 4:A sprinter starts from rest and accelerates at 3.5-m/s2 for 9.5-s. What is the runners speed after that time?

Know:vi = 0-m/st = 9.5-sa = 3.5–m/s2

Find:

vf = ?

Formula: Solve:

atvv if sm

f

f

v

v

25.33

)5.9)(5.3(0