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

Answer:

#|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.