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 #?

1 Answer
Dec 18, 2016

Answer:

#|v(t)|=|1-pi/2| ≈ 0.57# (units)

Explanation:

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, #40m/s# is a speed, but #40m/s# west is a velocity.

Velocity is the first derivative of position, so we can take the derivative of the given position function and plug in #t=3# to find the velocity. The speed will then be the magnitude of the velocity.

#p(t)=t-cos(pi/2t)#

#p'(t)=v(t)=1+pi/2sin(pi/2t)#

The velocity at #t=3# is calculated as

#v(3)=1+pi/2sin((3pi)/2)#

#v(3)=1-pi/2#

And then the speed is simply the magnitude of this result, such as that speed= #|v(t)|#

#|v(t)|=|1-pi/2| ≈ 0.57# (units)