Question

1.8 pts Question 4 Three experimental vehicles are compared in a race where each vehicle is allowed one gallon of fuel. The three Vehicles start at the same time and travel in the same direction along a straight, flat road. Each vehicle travels until it is out of fuel. The figure below shows the velocity, v of each vehicle as a function of time. Choose the correct statement below. 1u(t) (mph) Vehicle A Vehlele Vehicle B 2 ts ty ? (hours) Up to time ty vehicle C had traveled the greatest distance, Up to time ty vehicle B had traveled the greatest distance, Vehicle B traveled the greatest distance overall. Vehicle C traveled the greatest distance overall. Vehicle A traveled the greatest distance overall,

Answer 1

Observe that the velocity of all 3 of the cars is always positive. Thus the distance traveled by the cars is same as the displacement. But the displacement is given by the area under the curve of velocity vs time graph as

$s=\int v\; dt$

Up until the time $t_2$ , the area under the velocity vs time graph is maximum for the car . Thus car covers the maximum distance up until the time $t_2$ . Thus options 1 and 2 are incorrect.

Overall the area under the velocity vs time graph is maximum for the car . Thus car covers the maximum distance overall. Thus option 4 is correct (and hence options 3 and 4 are incorrect).