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Published byDinah Hancock Modified over 3 years ago

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What is acceleration? My speedometer:

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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.

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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

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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

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So, what would this mean? What would I see on my speedometer?

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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 second 20 mph at 2 seconds 30 mph at 3 seconds, etc.

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What would my speed-time graph look like?

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Can you understand you would get this shape? You would get a linear shape

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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.

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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

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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)

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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

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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 (t 2 ) 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 8 2 = 320 miles·sec/hour (don’t worry about the units)

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

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With constant speed, these graphs appear linear

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

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

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

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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.

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

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

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