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 $t = 7$ ?

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Answer 1 · 2017-07-12T15:02:42

$"speed" = 8.94$ $"m/s"$

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.

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