The position of an object moving along a line is given by #p(t) = 2t - 2tsin(( pi )/4t) + 2 #. What is the speed of the object at #t = 7 #?

1 Answer
Jul 12, 2017

Answer:

#"speed" = 8.94# #"m/s"#

Explanation:

We're asked to find the speed of an object with a known position equation (one-dimensional).

To do this, we need to find the velocity of the object as a function of time, by differentiating the position equation:

#v(t) = d/(dt) [2t - 2tsin(pi/4t) + 2]#

#= 2 - pi/2tcos(pi/4t)#

The speed at #t = 7# #"s"# is found by

#v(7) = 2 - pi/2(7)cos(pi/4(7))#

#= color(red)(-8.94# #color(red)("m/s"# (assuming position is in meters and time in seconds)

The speed of the object is the magnitude (absolute value) of this, which is

#"speed" = |-8.94color(white)(l)"m/s"| = color(red)(8.94# #color(red)("m/s"#

The negative sign on the velocity indicates that the particle is traveling in the negative #x#-direction at that time.