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 #?
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:
(I've assumed proficiency with the product and chain rule)
Therefore the speed at