When jumping, a flea reaches a takeoff speed of 1.0 m/s over a distance of 0.47 mm. What is the flea's acceleration during the jump phase?

We can use kinematics here if we assume a constant acceleration (not realistic, but they want a single value answer, so it's implied). We know final velocity, vf, is 1.0 m/s, and we cover a distance, d, of 0.47mm or 0.00047 m (1m = 1000mm for conversion). We also can assume that the flea's initial velocity, vi, is 0 at the beginning of its jump. Using the equation vf^2 = vi^2 + 2ad, we can solve for our acceleration, a. Like so: a = (vf^2 - vi^2) / 2d = (1.0^2 - 0^2) / (2*0.00047) = 1,064 m/s^2, not bad for a flea!