A mouse moves back and forth within a straight tunnel, attracted to bits of whit

Question

A mouse moves back and forth within a straight tunnel, attracted to bits of white cheddar cheese introduced to and removed from the left end and right end of the tunnel. The graph of the mouse's velocity, v, is shown in the graph at left. Positive velocity indicated motion to the right in the tunnel while negative velocity shows movement to the left in the tunnel. Assuming that at t = 0 the mouse is in the center of the tunnel, use the graph to estimate (and supply remarks showing why you made the choices you did) all the times at which: A] the mouse changes direction. B] the mouse is moving most rapidly to the right. C] the mouse is the most left of center. D] the mouse's speed is decreasing. E] the mouse is at the center of the tunnel.

Explanation / Answer

Solution:

A) The mouse changes direction from : Right to Left at t=15Sec (Positive Velocity to Negative Velocity)

Left to Right at t = 23Sec (approx) (Negative Velocity to Positive Velocity)

again Right to Left at t = 25Sec (approx) (Positive Velocity to Negative Velocity)

B) The mouse is moving most rapidly to right at t = 23Sec (approx) as the curve is more steep at this time to t= 25Sec

C) The mouse is most left of center at t = 0Sec

D) The mouse's speed is decreasing: From t = 10Sec to t = 15Sec

From t = 20Sec to t = 23Sec

and From t = 24Sec to t = 26Sec (approx)

E) The mouse is at the center of the tunnel: t = 0Sec, 15Sec, 23Sec, 26Sec (aprox) (The positions where directions are changing)

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