Question

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`?

Answer 1

`|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.