The position of an object moving along a line is given by #p(t) = 2t - cos(( pi )/6t) #. What is the speed of the object at #t = 7 #?

1 Answer
Jul 15, 2017

Answer:

#v = 1.74# #"LT"^-1#

Explanation:

We're asked to find the speed of an object moving in one dimension at a given time, given its position-time equation.

We therefore need to find the velocity of the object as a function of time, by differentiating the position equation:

#v(t) = d/(dt) [2t - cos(pi/6t)] = 2 + pi/6sin(pi/6t)#

At time #t = 7# (no units here), we have

#v(7) = 2 + pi/6sin(pi/6(7)) = color(red)(1.74# #color(red)("LT"^-1#

(The term #"LT"^-1# is the dimensional form of the units for velocity (#"length"xx"time"^-1#) . I included it here because no units were given.