Question

Two cars are traveling down a one way street, but they are traveling in opposite directions! The first car is initially driving at 13 m/s and the second car is initially driving at 36 m/s. When the two cars are 130 m apart, the drivers both realize they need to hit the brakes if there is any hope of avoiding a collision. Both drivers immediately hit the brakes.

(a) If the first car decelerates at a rate of 2.5 m/s 2 and the second car decelerates at 1.50 m/s 2 , will the two cars collide? If so, at what location will the cars collide. If not, how far apart are the two cars when they both come to a complete stop?

(b) On a single graph, plot the position of the two cars as a function of time. For your graph, define x = 0 to be the position of the first car at the moment both vehicles slam on their brakes, and draw both lines until the time(s) when the vehicles collide (if they do) or brake to a stop. Clearly label your axes, indicate the scale of your plot, and identify each car’s plot on the graph.

(c) On a single graph, plot the velocity of the two cars as a function of time. Clearly label your axes, indicate the scale of your plot, and identify each car’s plot on the graph.

(d) Can you use the plots in (b) and (c) to determine whether the two cars will collide? If so, how. If not, why not?

Answer 1