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Physics LibreTexts

8.3: Acceleration

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In a similar way, we can take the derivative velocity with respect to time to get acceleration, which is the second derivative of x with respect to t :

a=dvdt=d2xdt2

SI units of acceleration are meters per second squared (m/s2).

Example. In the previous example, we found a formula for the velocity of a particle as v(t)=10t. The acceleration of the particle in this example is a(t)=10 m/s2, a constant.

As we'll see later when we discuss gravity, all objects at the surface of the Earth will accelerate downward with the same acceleration, 9.80 m/s2. This important constant is called the acceleration due to gravity, and is given the symbol g :

g=9.80 m/s2(=32ft/s2).

This value is an average for the Earth; for a more exact value of g, you can use Helmert's equation (Section 51.4).

The acceleration due to gravity gives rise to a common (non-SI) unit of acceleration, also called the g :

1 g=9.80665 m/s2.

This number is a standardized conventional value that has been adopted by international agreement.


8.3: Acceleration is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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