velocity of spring

**keemariee** · May 14th 2008, 03:29 PM

A mass attached to a vertical spring has position function given by s(t)=5sin(3t) where t is measured in seconds and s in inches.
Find velocity at time t=4.
Find the acceleration at time t=4.

**TheEmptySet** · May 14th 2008, 03:34 PM

Originally Posted by keemariee

A mass attached to a vertical spring has position function given by s(t)=5sin(3t) where t is measured in seconds and s in inches.
Find velocity at time t=4.
Find the acceleration at time t=4.

velocity is the first derivative of position and acceleration is the 2nd derivative of postition so

$v(t)=\frac{ds}{dt}=15\cos(3t)$

$v(4)=15\cos(12)$

$a(t)=\frac{dv}{dt}=45\sin(3t)$

$a(4)=45\sin(12)$

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