For 0

Question

For 0<t<12, 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

amistre64 · Answer

x(t) is an integration of v(t)

luigi0210 · Answer

Find the acceleration of the particle at time t. Is the speed of the particle increasing, decreasing or neither at time t=0 to time t=6

amistre64 · Answer

well, acceleration is the derivative of v(t)

luigi0210 · Answer

How would I determine whether or not it is speeding up or not?

luigi0210 · Answer

*at time t=4?

amistre64 · Answer

if acceleration is 0, velocity is constant.

when acceleration is negative, we are slowing down, when acceleration is positive we are speeding up

amistre64 · Answer

v(t)=cos((pi/6)t) , what is the derivative of this?

luigi0210 · Answer

$$\frac{ \Pi }{ 6} * -\sin(\frac{ \Pi }{ 6 }t) ?$$

amistre64 · Answer

yes, now when t=4, we end up in the 2nd quadrant where sin is positive.

-pi/6 * something postive gives a negative result for our acceleratio

luigi0210 · Answer

Would a sign pattern help?

amistre64 · Answer

it might help you, but i already have a solution regarding the acceleration at t=4