Scientists have studied two species of sand lizards, the Mojave fringe-toed lizard and the western zebra-tailed lizard, to understand the extent to which the different structure of the two species' toes is related to their preferred habitats-fine sand for the Mojave lizard and coarse sand for the zebra-tailed lizard. (Figure 1) shows a somewhat simplified velocity-versus-time graph for the Mojave fringe-toed lizard.

Question

estimate the maximum acceleration of the lizard in m/s and g's

Answer 1

To estimate the maximum acceleration of the lizard, we can look at the steepest part of the velocity-vs-time graph. The maximum acceleration occurs when the velocity is changing at its fastest rate.

To estimate the maximum acceleration in m/s, we need to determine the slope of the steepest part of the graph. The slope represents the rate of change of velocity, which is equal to acceleration. We can choose a couple of points on the steepest part of the graph and calculate the slope.

Let's say we choose two points: (t1, v1) and (t2, v2).

The slope, or acceleration, is given by the formula:

acceleration = (v2 - v1) / (t2 - t1)

Looking at Figure 1, it seems that the steepest part of the graph occurs between approximately t = 0.2 s and t = 0.35 s. Let's choose two points on this segment as an example: (0.2 s, 2 m/s) and (0.35 s, 11 m/s).

Using the formula for acceleration, we can calculate:

acceleration = (11 m/s - 2 m/s) / (0.35 s - 0.2 s)
= 9 m/s / 0.15 s
= 60 m/s^2

Therefore, the estimated maximum acceleration of the lizard is 60 m/s^2.

To estimate the maximum acceleration in g's, we need to divide the acceleration in m/s^2 by the acceleration due to gravity, which is approximately 9.8 m/s^2.

acceleration in g's = (60 m/s^2) / (9.8 m/s^2)
≈ 6.12 g's

Therefore, the estimated maximum acceleration of the lizard is approximately 6.12 g's.