Question

The position of an object moving along a line is given by `p(t) = 4t - tsin(( pi )/8t)`. What is the speed of the object at `t = 3`?

Answer 1

In one dimension, speed is just the magnitude of velocity, such that if we had a negative value we would just take the positive version.

To find the speed function, we will need to differentiate the position function with respect to t:

Let `s(t)` be the speed function:
`s(t)=4-sin(pi/8t)-pi/8tcos(pi/8t)`
(I've assumed proficiency with the product and chain rule)

Therefore the speed at `t=3` is given by:
`s(3)=4-sin(3pi/8)-3pi/8cos(3pi/8)`
`s(3)=2.63ms^-1` (ensuring the take the trig functions in radians)