1. ## Velocity

" An object moves along the x-axis with initial position x(0) = 2

The velocity of the object at time t>/= 0 is given by v(t) = sin(pi/3t)

A: for 3< t < 4.5 the velocity of the object is decreasing
B: for 3< t < 4.5 the speed of the object is increasing

Are either both of these statements correct? For each statement provide a reason why it is correct or not.

What is the position of the object at time t=4? "

2. Differentiate v(t) with respect to t to find the acceleration, a(t). The velocity is decreasing if a(t) < 0 and increasing if a(t) > 0. The speed is increasing if either v(t) > 0 and a(t) > 0, or v(t) < 0 and a(t) < 0; it is decreasing if v(t) and a(t) have opposite signs.

To find the position, you need to integrate v(t) with respect to t.

3. Originally Posted by JC1341
" An object moves along the x-axis with initial position x(0) = 2

The velocity of the object at time t>/= 0 is given by v(t) = sin(pi/3t)

v(t)=sin( (pi/3) t )

or

v(t)=sin( pi/(3t) )

The first seems more likely, but don't make us guess.

(if you don't want to differentiate whatever you do mean, you could
try sketching the velocity time curve)

RonL