" 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? "
help please, thanks
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.
Please be more carefull with your notation. Do you mean:
Originally Posted by JC1341
v(t)=sin( (pi/3) t )
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)