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Virtual Car: Velocity and Acceleration

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Interactive

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This interactive activity developed for Teachers' Domain demonstrates how vectors are used to represent velocity (speed and direction) and acceleration. In the activity, vectors change in real time as you "drive" a car on a flat plain; as you change speed and direction, vectors originating from the car respond to your actions. A graph depicting speed vs. time also responds to your actions, displaying both the speed and acceleration of the car.

Background Essay

Imagine that you're in a car traveling at a high speed and accelerating quickly. You're heading directly toward a brick wall, and you continue to accelerate until you reach that wall. Sounds like you're in a heap of trouble, doesn't it? Not necessarily. When we hear the word acceleration, we usually assume it means "increasing in speed." In many cases, that's exactly right. But in physics, acceleration is defined as "a rate of change of velocity." This change can be either an increase or a decrease in speed, or a change in direction. In the example given here, acceleration refers to a decrease in speed, so the car decelerates as it approaches the brick wall, slowing down until it gently bumps into it.

Just as acceleration has a precise meaning in physics, so do the terms speed and velocity. While it's perfectly acceptable at times to use the two terms interchangeably, each can have its own distinct meaning. Speed is defined as the rate of motion and is calculated by dividing the distance an object travels by the time it takes to travel that distance. Velocity, on the other hand, is a vector quantity -- a measurement of both the rate of motion (i.e., speed) plus direction. In other words, ten kilometers per hour is speed; east at 10 kilometers per hour is velocity.

Speed, velocity, and acceleration are sometimes depicted graphically. A graph illustrating time vs. speed, for example, provides a record of how the speed of an object changes over time. From such a graph, it's also possible to see whether an object is traveling at a constant rate or accelerating: A line parallel to the time axis isn't changing its speed, while one that's slanted is.

Another way to depict motion graphically is with arrows. Remember we said that velocity is a vector quantity? Another fact to know is that vector quantities can be described by both magnitude and direction. To represent velocity, an arrow's length can show the speed at which an object is traveling (magnitude, or the rate of acceleration), and its orientation can show the object's direction. Acceleration, which is described by a magnitude and a direction, is itself a vector quantity. (Force and distance are two other vector quantities.)

It's possible for an object to be moving at a constant speed and be accelerating at the same time. Take as an example a car driving in a circle at 30 kilometers per hour. Although its speed is constant, its velocity is continually changing because its direction is continually changing as well. This change of direction results in an acceleration toward the center of the circle. Likewise, a satellite in circular orbit around Earth is traveling at a constant speed and accelerating toward Earth's center.

Engineers who design cars are keenly aware of acceleration resulting from a change in direction. With safety in mind, they use tires that provide enough friction to keep their cars from losing control when rounding corners. To increase the friction force for a fast-moving car, some engineers design the car's body shape to "hug" the ground. When moving fast enough, the car's body deflects air upward, forcing the car downward. This downward push increases the friction force between the tires and the ground.

Discussion Questions

• What is the difference between speed and velocity?
• Define acceleration. What does it mean besides an increase in speed?
• What if the graph showed acceleration rather than speed? Where would the line be when the car was continuing at a constant speed of 40 mph in the same direction? Where would the line be if the speed were continually increasing? Decreasing?
• An object, such as a planet, circling another object, such as the Sun, at a constant speed is said to be accelerating. Explain why this motion is an example of acceleration.

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