A glider attached to one end of a string oscillates given by the displacement function x(t) = 0.030cos(4.00t) is the acceleratio

Question

3 years ago

11

n of the mass after 3.56 seconds ?

1 answer:

devlian [24] · Answer 1 · 2022-09-18T22:15:05+03:00

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)

<u></u>

Learn more about acceleration here: