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Acceleration is defined as the change in velocity over time--how much an object speeds up or slows down. ("Deceleration" is the term usually used to describe negative acceleration-slowing down.) Velocity is the rate, or speed, at which an object moves over time. Mathematically, velocity is defined as the distance traveled divided by the time taken to travel that distance. For instance, an airplane that travels 50 feet in one second has a velocity of 50 feet per second, or v = 50 ft/sec. Velocity is often expressed in miles per hour or kilometers per hour-an automobile travels 60 miles per hour-it takes it one hour to travel a distance of 60 miles.

Acceleration is the change in velocity divided by the time taken to make the change. For example, if an airplane's speed increases from 50 ft/sec to 60 ft/sec and it takes five seconds to make that change, the change in velocity during this time is 10 ft/sec (60 ft/sec - 50 ft/sec). To find the acceleration, we simply divide this change (10 ft/sec) by the time it takes to make this change--5 seconds: "10 divided by 5 is 2."

As for the units, ft/sec divided by seconds is the same as multiplying by 1/sec, which results in ft/(s x s) or ft/s2. So, the acceleration of the airplane is 2 ft/sec2. Acceleration is also a vector, meaning it has a value and a direction.

formular for calculating acceleration

Therefore, to calculate the acceleration of a car going from 0 mph to 60 mph in 10 seconds, we must first convert miles per hour to feet per second in order to divide the change by 10 seconds. By performing the computations to convert miles to feet and hours to seconds, we are left with the appropriate velocity in ft/sec.

formular for computing velocity

We now divide 88 feet/second by the amount of time taken to make the change, which was 10 seconds. 88 ft/sec divided by 10 seconds shows the acceleration to be 8.8 ft/sec2.

The method is the same when using the metric system: meters replace feet and kilometers replace miles (using the correct conversion factors for actual distances).