Question

PLEASE HELP AND EXPLAIN

A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)
a) find the acceleration a(t) of the particle at any time.
b) find all values of t, 0 13 years ago

Answer 1

So the acceleration is given by the change in velocity over time right?

Answer 2

yes

Answer 3

\(a = \frac{dv}{dt}\) Which means that we need to differentiate our current formula for velocity to find the equation for acceleration, ok?

Answer 4

okay, i understand that. i just need help getting the derivative of it.

Answer 5

Ok, so first step is to split in to terms. Here the 1 just becomes 0 when we differentiate so we are really just concentration on the sin term.

Answer 6

Lets take the - out too to make our lives easier. leaving\[(-1) \frac{ d }{ dt }(\sin(2\pi t))\]With me so far?

Answer 7

yes, because the -1 just becomes 0.

Answer 8

Use a substitution on the term making u=2 pi t. And then use the chain rule to end up with \(a(t)=-2 \pi cos(2\pi t)\)

Answer 9

so if u=2pit, do i need to find u'?