The position of an object moving along a line is given by p(t) = 2t - 3cos(( pi )/2t) + 2 . What is the speed of the object at t = 3 ?

1 Answer
Nam D.
May 7, 2018

(-3pi)/2+2

Explanation:

The position function of the object is given by:

p(t)=2t-3cos(pi/2t)+2

Since the velocity is displacement over time, it means that it the rate of changing the position over time, or the derivative of the function.

Then we got,

v(t)=p'(t)

Let's find the hardest part, which I think is:

d/dt(3cos(pi/2t))

We get:

=3d/dt(cos(pi/2t))

=3d/dt(cos((pit)/2))

Let u=(pit)/2,:.(du)/dt=pi/2.

Then, y=cosu,:.dy/(du)=-sinu.

Combine to get:

=-sinu*pi/2

=-sin((pit)/2)*pi/2

=-pi/2sin((pit)/2)

So,
d/dt(3cos(pi/2t))=(-3pi)/2sin((pit)/2)

And now, we get:

p'(t)=2-[(-3pi)/2sin((pit)/2)]+0

=(3pi)/2sin((pit)/2)+2

So, at t=3, we get:

=(3pi)/2sin((3pi)/2)+2

=(-3pi)/2+2

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