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.