The position of an object moving along a line is given by #p(t) = 2t - sin(( pi )/6t) #. What is the speed of the object at #t = 4 #?

1 Answer
Apr 9, 2016

Answer:

Speed at t = 4:
#v=2.26 m.s^(-1)#

Explanation:

If we are given position as a function of time, then the function for speed is the differential of that position function.

Differentiate p(t):
• Differential of #asin(bt) = abcos(bt)#
#v(t)=(dp(t))/(dt) = 2 - π/6cos(π/6t)#

Now substitute in the value of t to find the value of speed at that time (t = 4):
#v(4) = 2 - π/6cos(π/6× 4) = 2.26 m.s^(-1)#