Bob is standing at rest. Wendy runs past him at a constant speed of 3.00 m/s. At the instant that Wendy passes him, Bob starts to run after her with a constant acceleration of 0.200 m/s How far must Bob run before he catches up with Wendy

90 meters

Explanation:

To find the distance in which Bob catches up with Wendy, you first write down the motion equations of both Bob and Wendy.

Wendy has a constant speed, then you have:

          (1)

Bob has an accelerated motion, then, his equation of motion is:

         (2)

v1: constant speed of Wendy = 3.00 m/s

v2: initial speed of Bob = 0 m/s

a: acceleration of Bob = 0.200m/s^2

When Bob catches up with Wendy x1 = x2, then you equal both equations and solve for time t:

you replace the values of a and v1:

Finally, you replace this value of time either the equation for x1 or the equation for x2, and you calculate the distance:

hence, Bob catches up with Wendy for a distance of 90m

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explanation:

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