The position of an object moving along a line is given by p(t) = 4t - sin(( pi )/4t) . What is the speed of the object at t = 1 ?

1 Answer
Sep 27, 2017

4-pi/(4sqrt2)

Explanation:

Position of an object p(t)=4t-sin(pi/4t)

Speed is defined as the rate of change in position of object with respect to time.
To find the speed we need to differentiate p(t) with respect to t.
speed =d/dt(p(t))
v=d/dt(p(t))=d/dt(4t-sin(pi/4t))
v=4-(pi/4)cos(pi/4t)

At time t=1
v_(t=1)=4-(pi/4)cos(pi/4(1))=4-pi/4(1/sqrt2)=4-pi/(4sqrt2)