How to Calculate a Speed Equation
- 1). Record how long it takes the object to move across whatever space you are monitoring. If you throw a baseball, for example, record the amount of time it took for the baseball to land. If you're working on questions from physics class, you'll generally receive this information as part of the question.
- 2). Determine how far the object moved. If you know its starting and final locations, you can subtract start from finish. Alternatively, if you have an object like a ball that came to rest on the ground, you can measure the distance from where you stood to where the ball landed.
- 3). Divide the distance moved by the time elapsed to find average speed. For example:
If a baseball flies 10 meters before coming to rest in a time of 2 seconds, what was its average horizontal speed? Answer: 10/2 = 5 meters per second.
If speed remains constant, then average speed is the speed of the object at every point during the duration of its travel. In this case, you're done. In many cases, however, speed varies with time, so the average speed and the instantaneous speed are not the same. With our baseball, for example, the horizontal speed -- speed relative to the ground -- decreases slightly due to air resistance. This effect is negligible enough, however, that we can assume average horizontal speed and instantaneous horizontal speed are the same. Its vertical speed, however, changes rapidly during its flight. At first the baseball is headed up, and later on it's headed down. In a case like this, where speed is changing with time, we can calculate instantaneous speed if we know acceleration. - 4). Determine the acceleration of the object during its travel. For physics class questions, you'll typically receive this information. If you're measuring the speed of a baseball or other projectile under the influence of gravity, however, you can assume that the vertical acceleration of any object near Earth's surface is 9.81 meters per second squared. This is not true if an object (a feather, for example) experiences substantial air resistance as it falls, but in general it will be true.
- 5). If acceleration is constant, as in the case of gravity, then the speed of the object is equal to its initial speed plus acceleration times time. The vertical speed of the baseball, for example, is as follows:
Instantaneous vertical speed = initial vertical speed - 9.81 x time elapsed.
Notice that acceleration due to gravity is negative because gravity pulls the object downward, decreasing its vertical speed. - 6). Plug in the initial speed and time elapsed to find instantaneous speed. In the baseball example, for instance, if the baseball had an initial vertical speed of 5 meters per second upward, and 2 seconds have elapsed, we would find the following:
Instantaneous vertical speed = 5 - 9.81 (2) = -14.62 meters per second.
So after 2 seconds the baseball is falling at -14.62 meters per second, unless it has already struck the ground.
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