What is acceleration?

• My speedometer:

Acceleration occurs when speed changes

• Now we don’t want our cruise control on

• We want to use our gas pedal or brake to make our car go faster or slower.

Let’s start out with an new type of graph

This graph is called a velocity-time graph (also called a speed-time graph)

• Now we can show how the car’s speed changes

• We can get different shapes on the graph depending on how the speed changes

Think about this: Let’s say we are at a stopped light stopped. It turns green and we speed away. Let’s

say that we speed up 10 miles per hour per second. We can see this change with a speedometer.

• Our speedometer needle is going up

So, what would this mean?

What would I see on my speedometer?

If my car is increasing its speed at 10 mph / second, I would see it say:

* 0 mph at 0 seconds (started my stopwatch)10 mph at 1 second20 mph at 2 seconds

30 mph at 3 seconds, etc.

What would my speed-time graph look like?

Can you understand you would get this shape?

You would get a linear shape

This is the mathematical definition of acceleration

We can draw a line And we can get the slope of that line.

• This slope is the acceleration.

• It is defined as the slope of the line formed on a speed-time graph

• Our slope is this case is 10 mph/sec or we can say that every second my speed increases by 10 mph.

For this we can generate an equation.

• This equation is called our ‘how fast’ equation:• V = a(t), the velocity of the car is the

acceleration (a) x time.

• For example in my car ‘how fast’ is my car traveling at the end of 8 seconds?

• V = a x (t) = 10 x 8 or 80 mph

So we are getting faster

• This is obvious to you drivers, right? You can press on the gas and get the car to go faster and faster.

• We now know that the speed of the car can be found using the how fast equation

• Speed or Velocity, V = a x (t)

But what about ‘how far’ the car moves?

• It turns out we can develop an equation for this, too.

• This is the distance that the car moves

• On my fit and on your car, you have an odometer which can help us measure distances we drive

Odometer below the speedomter

We can determine the ‘how fast’ equation.

• In a real physics class, we would develop this equation; however, I will give it to you now.

• Distance = ½ x (a) x (t2)• Distance is one-half times the acceleration x

the square of time.• How far would my car go in 8 seconds?• Distance = ½ x 10 x 82 = 320 miles·sec/hour• (don’t worry about the units)

We can show our movement on a distance-time graph (also called a position-time graph). We have studied these already.

With constant speed, these graphs appear linear

However, now my car is not keeping one speed, its speed is increasing

If we made a distance-time graph now, it would appear curved

This shape is called a PARABOLA. We call this our getting faster parabola because

the car is getting faster

What does this parabola mean?• My distance is

INCREASING over successive time intervals.

• For example, if my car was traveling at 60 mph constant speed, every every hour I would travel 60 miles.

• Now my distance doesn’t stay constant, it increases.

What about my car getting slower? This is acceleration, too, because my speed is

changing.

We get a different looking parabola now and will study this later