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Acceleration: Definition, Equation and Examples

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  • 0:01 Cheetah Drag Racing
  • 0:33 Acceleration
  • 2:50 Solving Acceleration Problems
  • 5:30 Lesson Summary
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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

Acceleration can be a tricky topic for many students who tend to get hung up on an object's speed. In this lesson, we will explore the common aspects of acceleration and why speed is not always important.

Cheetah Drag Racing

I'm sorry if you've heard this one before, but the cheetah is the king of fast. At its best, a cheetah can run over 100 km/hr. By itself, this is an incredible feat. But what I find even more incredible is that the cheetah is able to be standing still one second and three seconds later it's running 100 km/hr! Most of your high-end cars require between four and six seconds to do what that cheetah does in three seconds. And with this quick analogy, we can get to the meat of this lesson: acceleration.

Acceleration

Acceleration is the rate of change of an object's velocity. Remember, velocity is how fast an object is moving in a specific direction. So, acceleration measures how fast the velocity changes. We can calculate acceleration if we know the total change in velocity and the time it takes for the velocity to change. The equations are:

Average acceleration = change in velocity / change in time

Change in velocity = final velocity - starting velocity

The units for acceleration are m/s^2, but something else is required. Acceleration, like velocity, is a vector quantity. This means that you need to specify the direction of motion as well. This could be a compass point, like north and east, or a simple description like right or left or up or down, depending on the question. In addition, acceleration can be positive or negative. If a car, for example, is traveling in a straight line and its speed increases, the acceleration is positive. If that car slows down, its acceleration is negative.

I want to pause for a minute here to clarify a couple of points. First, in everyday usage, acceleration has come to mean speeding up. If you press on the accelerator in your car, the car's speed increases. Acceleration has a slightly different meaning in physics, though. The definition specifically mentions a change in velocity, not speed.

Remember, velocity has a direction attached, so if the direction of travel changes, the velocity changes, even if the speed remains constant. Picture setting the cruise control on the car at 40 km/hr and driving in a circle. Speed is a constant 40 km/hr, but velocity changes every time you change direction. Since velocity is changing, you can calculate acceleration even though the speed is constant. Acceleration is not dependent on a change in speed.

The second point involves the term deceleration, commonly used to mean slowing down. The term deceleration is not commonly used in physics. Instead, deceleration is more often called negative acceleration.

Solving Acceleration Problems

Remember the cheetah from the introduction? Let's use what we just learned about acceleration to calculate the acceleration of the cheetah. We know that the cheetah has an initial velocity of 0 km/hr because he's standing still, stalking his prey. When he's ready to attack, he can reach a speed of 100 km/hr in 3 seconds. First, we need to convert kilometers per hour to meters per second.

100 km x 1000 m/km = 100,000 m

1 hour x 60 min/hr x 60 sec/min = 3600 seconds

100,000 m / 3600 sec = 27.8 m/s

The cheetah starts with a velocity of 0 m/s because he is not moving. He begins running west, after a gazelle, and reaches a maximum velocity of 27.8 m/s west in 3 sec.

Average acceleration = change in velocity / change in time

Average acceleration = (27.8 m/s west - 0 m/s) / 3 sec = (27.8 m/s west) / 3 sec = 9.3 m/s^2 west

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