The position of an object moving along a line is given by #p(t) = t-cos(( pi )/2t) #. What is the speed of the object at #t = 3 #?
Speed is a scalar quantity having only magnitude (no direction). It refers to how fast an object is moving. On the other hand, velocity is a vector quantity, having both magnitude and direction. Velocity describes the rate of change of position of an object. For example,
Velocity is the first derivative of position, so we can take the derivative of the given position function and plug in
The velocity at
And then the speed is simply the magnitude of this result, such as that speed=