The position of a particle moving along x-axis varies with time t as #4x + t^2 = 4#. At what position, the particle is at rest?

Question

x = 4

x = -2

x = 1

x = 2

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Answer 1 · 2017-11-20T02:49:39

Selection 3. x = 1

Given:

#4x + t^2 = 4#

Solve for x:

#4x = 4 - t^2#

#x = 1 - t^2/4" [1]"#

Compute the first derivative with respect to t:

#dx/dt = t/2#

The speed is 0 at the time(s) where the first derivative is equal to 0:

#t/2 = 0#

#t = 0#

To find the x coordinate, substitute 0 for t in equation [1] :

#x = 1 - 0^2/4#

#x = 1#

This corresponds to selection 3.