A turtle is traveling at a constant speed along a straight path of 10.0-m long s

Question

A turtle is traveling at a constant speed along a straight path of 10.0-m long set out for it by a turtle-studying biologist. The turtle travels at a constant speed of 0.12 m/s. The turtle began at the 0-m mark. However, the biologist forgot to start his stopwatch right away. When the turtle reaches the 3.0-m mark, the biologist's stopwatch reads 14.8-s.
Questions: Where was the turtle when the biologist remembered to turn his stopwatch on? What is the reading on the biologist's stopwatch when the turtle reaches the 10.0-m mark?

Explanation / Answer

1. Let's call the position where the turtle was initially at when the biologist turned on the stopwatch x0, or the initial position (this is the quantity we want to find). We know that 14.8 seconds pass, so we'll say that the time elapsed, t, is equal to 14.8 s. Also, we know that, at the end of the elapsed time, the turtle is at the 3.0 m, so its final position, xf, is 3.0 m. In addition, we know that the turtle moves at a constant velocity, v, of 0.12 m/s throughout this whole time.

We know from kinematics (with no acceleration):

xf = xi + vt

Solving for xi and substituting values:

xi = xf - vt = (3.0 m) - (0.12 m/s) (14.8 s) = 1.224 m 1.2 m

2. Let's call tf the time recorded on the biologist's stopwatch when the turtle reaches the 10.0 m mark (the time we wish to solve for). We know that the biologist started his stopwatch from when the turtle started at 1.224 m into the travel. Therefore, we must solve for the time it took for the turtle to get from this 1.224 m spot to the 10.0 m mark. This displacement, x, is found by subtracting the starting location (1.224 m) from the final location (10.0 m). Therefore, x = (10.0 m - 1.224 m) = 8.776 m. Also, we know that, throughout this time, the same turtle has been walking with the constant velocity, v, of 0.12 m/s.

We can use a similar kinematics equation (knowing that acceleration is constantly zero):

x = vtf

Solving for tf and substituting values:

tf = x / v = (8.776 m) / (0.12 m/s) = 73.13333... s 73 s

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