Question

A glider attached to one end of a string oscillates given by the displacement function x(t) = 0.030cos(4.00t) is the acceleration of the mass after 3.56 seconds ?

Answer 1

This question involves the concepts of the derivatives, displacement, velocity, and acceleration.

The acceleration of mass after 3.56 s is "-0.465 m/s²".

First, we will find the velocity function by taking the derivative of the displacement function with respect to time:

$\frac{d}{dt}x(t)=v(t)=\frac{d}{dt}[0.030\ Cos(4t)]\\\\v(t)=-0.12\ Sin(4t)$

Now, we will find the acceleration function by taking the derivative of the velocity function with respect to time:

$\frac{d}{dt}v(t)=a(t)= \frac{d}{dt}[-0.12\ Sin(4t)]\\\\a(t)=-0.48\ Cos(4t)$

At t = 3.56 s:

a(3.56) = -0.48 Cos(14.24)

a(3.56) = - 0.465 m/s²

Learn more about acceleration here:

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