# Velocity

• Dec 19th 2007, 03:38 PM
JC1341
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? "

• Dec 19th 2007, 04:31 PM
JaneBennet
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.
• Dec 19th 2007, 11:57 PM
CaptainBlack
Quote:

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)