Question

miles challenges an elephant to a drag race (straight track with no turns) using go - karts. assuming that the go - cart wouldnt break under the weight of the elephant and that the go - karts have identical amounts of power, who would you expect to win?
a elephant
b miles
c the race would end in a tie.
d theres not enough information to tell.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). Power \(P=\frac{W}{t}=\frac{Fd}{t}=Fv\) (assuming constant force and velocity in the short - term for a drag - race start, \(W\) is work, \(t\) is time, \(d\) is distance). Since power \(P\) is the same for both go - karts, and \(P = Fv\), and initially \(v = 0\) (start of the race), we can consider the force \(F\). If \(P\) is constant, and at \(v = 0\) (start of the motion), we can relate to the force - mass - acceleration relationship. Given \(P\) is the same, and \(F=\frac{P}{v}\) (as \(v\) approaches \(0\), we can think in terms of the maximum force. Assuming the power is used to overcome inertia (start moving), from \(F=ma\), \(a=\frac{F}{m}\). The elephant has a larger mass \(m\) than Miles.

Step2: Analyze acceleration

If the force \(F\) (related to power) is the same (since go - karts have identical power) at the start of the race (when \(v\) is very small, power \(P = Fv\) implies that the maximum force available is similar for a very low \(v\)), and \(a=\frac{F}{m}\). Since \(m_{elephant}>m_{Miles}\), then \(a_{Miles}>a_{elephant}\) (because \(F\) is approximately the same at the start of the race for the two go - karts with the same power). A larger acceleration means that Miles' go - kart will start moving faster and will win the drag race (a short - distance, straight - track race where initial acceleration is crucial).

Answer:

B. Miles