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At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.50 $\mathrm{m} / \mathrm{s}^{2} .$ At the same instant, a truck, traveling with a constant speed of $15.0 \mathrm{m} / \mathrm{s},$ overtakes and passes the automobile. (a) How far beyond its starting point does the automobile overtake the truck? (b) How fast is the automobile traveling when it overtakes the truck?

a) 180 $\mathrm{m}$b) 30 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

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University of Michigan - Ann Arbor

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Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

03:24

At the instant the traffic…

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01:45

Additional ProblemsAt …

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08:40

06:33

05:17

Acceleration At the instan…

02:27

A car in the northbound la…

04:38

A $1000 \mathrm{~kg}$ auto…

05:25

01:15

A truck is stopped at a st…

So we have an acceleration of the motorcycle, 202.5 meters person meters per second squared and we have the velocity of the truck initially, which equals the velocity of the truck final and this equals again 15.0 meters per second. So essentially the scenario is that the motorcycles at the stoplight and it's accelerating once it turns green. However, the truck right Leslie red as the light turns green, passes the motorcycle with a with a speed of 15.0 meters per second. So part ay is going is asking us to find the time it takes for the motorcycle to reach the truck. So we can say that Delta X is going to be equal to the ex initial t close 1/2 a t squared. We know that this equal zero for the motorcycle so Delta X will equal 1/2 80 squared for the motorcycle Now, during this time interval, the truck is also still moving. So Delta actually equal v X is he for the truck? So we can simply say that of the X T equals 1/2 80 squared and essentially combine these two equations and soul for tea. So we find that tea is equaling two times velocity in the ex direction, divided by the acceleration of the motorcycle. And this is equaling. Two times 15 divided by 2.5 and tea is equally 12 seconds. So essentially it takes 12 seconds for the motorcycle to catch up with the truck. Now it's asking how far ahead of these stop right of the inter protection. Rather, did they meet up with each other? So you can simply say that tow X equals V X initial times t. So this will be 12 times 15 and equaling 180 meters. And this is 180 meters ahead of the starting position of the motorcycle so we can say ahead of ex initial of the motorcycle. Um, so this would be another. This will be the second answer for party and then for part B. Rather, we could get a new what book for Part B. They want us to find the final velocity of the motorcycle as it as it passes the truck so the X final will be equal to the ex initial. Remember, the motorcycle started off at zero initial velocity because it was at the intersection, so that would be zero and this would be equal to 2.5 times the total time of 12 seconds. And this is equaling 30 meters per second. Again, this is for the motorcycle. This would be your answer for part B. That is the end of the solution. Thank you for watching.

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