Calculus Question:

For 0 12, ≤ ≤t a particle moves along the x-axis. The velocity of the particle at time t is given by

v(t) = cos(pi/6)t.
= The particle is at position x = −2 at time t = 0.
(a) For 0 12, ≤ ≤t when is the particle moving to the left?

Question

Calculus Question:

For 0 12, ≤ ≤t a particle moves along the x-axis. The velocity of the particle at time t is given by

v(t) = cos(pi/6)t.
= The particle is at position x = −2 at time t = 0.
(a) For 0 12, ≤ ≤t when is the particle moving to the left?

anonymous · Answer

they want to find t when x(t) < 0

as you may know, velocity as a function of time v(t) is the time derivative of distance as a function of time x(t). this means that x(t) is the anti-derivative of v(t).

$$x(t) = \int\limits_{}^{}v(t) dt = \int\limits_{}^{} \cos \left( \frac{ \pi }{ 6 }t \right) dt$$

this is step 1. can you tell me what the indefinite integral of that is?

anonymous · Answer

Oh okay I have to use integration :) That makes it so much easier than taking the derivative. Thanks.