The position of an object moving along a line is given by p(t) = t - tsin(( pi )/4t) . What is the speed of the object at t = 5 ?

1 Answer
Aug 26, 2016

|v(5)|=1+1/sqrt2+(5pi)/(4sqrt2).

Explanation:

The velocity of the particle at any time t is given by the derivative with respect to time of the position. In other words, v(t)=p'(t).

v(t)=p'(t)=1-sin(pi/4t)-tpi/4cos(pi/4t). (Note: to do this you must use the product rule).

v(5)=1-sin((5pi)/4)-(5pi)/4cos((5pi)/4)=1+1/sqrt2+(5pi)/(4sqrt2).

Speed is the absolute value of velocity, but the velocity here is positive so it's not an issue.