The light turns green, and at time t=0 the car starts moving and travels with a constant acceleration. At that instant a truck traveling at constant tốc độ v(truck) is alongside the car, with the front of each vehicle at position x=0. The truck passes the car, but the oto later catches up khổng lồ the truck in front of a house, such that at time (tD) the front of each vehicle is at position x=D.

A.On a velocity vs. Time graph, sketch và label graphs of the velocity of the car và the velocity of the truck as a function of time. Indicate any important velocities or times.

B.Two students are discussing how the tốc độ of the car compares to lớn the speed of the truck of when both vehicles are in front of the house.

Student 1"The distance traveled by the car và the truck is the same, và the time is the same, so they must have the same speed."

Student 2"I don’t see how that can be. The oto catches up khổng lồ the truck, so the car has to lớn be going faster”

Which aspects of Student 1’s reasoning, if any, are correct? tư vấn your answer with features of your graphs in part (a).

Which aspects of Student 2’s reasoning. If any, are correct? tư vấn your answer with features of your graphs in part (a).

C. Derive an expression for the acceleration of the car. Express your answer in terms of D và v(initial).

D. Determine the time at which the tốc độ of the car is equal lớn the speed v(truck) of the truck. Express your answer in terms of t(pointD). Justify your answer.

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A. V(truck) is horizontal, v(car) is a line with slope "a" (acceleration) beginning at the origin and crossing v(truck) somewhere between t = 0 và t = tD. (In fact, this "somewhere" is at t = tD / 2.)

B. Student 1 is correct only if we consider the car’s AVERAGE velocity, which is equal khổng lồ v(truck). At t = tD, the area under the rectangle created by v(truck) is equal lớn the area under the triangle created by v(car). Student 2 is correct for all those points where v(car) is greater than v(truck) — their intersection point.

C. This can’t be done — we were never given v(initial).

If you mean v(truck), then knowing the car’s velocity at t = tD is 2*v(truck) let’s us use Torricelli’s equation: v² = u² + 2aD

(2*v(truck))² = 0² + 2aD

a = 2*v(truck)² / D

D. I’ve already stated that v(car) = v(truck) at t = tD / 2.

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We know this because the average velocities must be the same, và so the car’s final velocity must be twice the truck’s velocity (since the oto started with zero velocity). Since the acceleration was constant, the velocities must be equal at the half-time point.

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This is a secured document question from AP college board & shouldn’t be published on a public website. It sounds like you are trying to help students cheat on private exams when you should help them learn physics. You make teaching và learning physics difficult when it is easier for students lớn just cheat.

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