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A car and a truck are heading directly toward one another ona straight and narrow street, but they avoid a head-on collisionby simultaneously applying their brakes at $t=0 .$ The resulting velocity-versus-time graphs are shown in $\mathrm{HGURE} 2-38$ . What is theseparation between the car and the truck when they have come torest, given that at $t=0$ the car is at $x=15 \mathrm{m}$ and the truck is at$x=-35 \mathrm{m} ?($ Note that this information determines which line inthe graph corresponds to which vehicle.)

11.25 $\mathrm{m}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

James M.

September 27, 2020

Carolina C.

October 11, 2020

Suppose the motion of a car corresponds to (Figure 1), with a velocity in the middle portion of V = 1.5 m/s

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Okay, So in this problem, we have this figure that represents the movement of a car and a truck when they try to stop to prevent a collision. Okay, So what? We know we know that the initial position off the car that's called the card green. Initial position of the car wasn't 15 meters, and the initial position of the truck was in minors. 35 meters. We need to prevent the collision, so they walk into our charter. Okay, So problem wants to discover the difference in position between the truck and the car. After this stuff, they managed to prevent a collision, and they want to discover what was the difference in position. Okay, we know this is a graph of velocity versus time, and every time we have a graph of velocity versus time and we need to discover the displacement, we just need to calculate the area under the curve. So here we have a triangle with dimensions 10 and 2.5. So that's thinking here the car have a displacement off 10 times, 2.5, divided by two. This is going to be equal to 12.5. So this is going to be draft 0.5 meters off displacement. Okay, so since he begins in the position 15 and he moving towards the truck, we're going to subtract 2.5 and then we have Let's see, 15 minutes trough 150.5. Visit grew 2.5 2.5, so the final position of the car was in 2.5 meters. What about the truck where we do the same thing? The displacement of the truck is just the triangle, the area under the curve off the truck. So we have a triangle off dimensions 15 and 3.5, but this is going to be 15 time 3.5, divided by two. So the displacement of the truck is just, uh let's see 26.25. So since the truck begin the position minus 2035 he moving in a positive direction. So we're going to some of 26 25 because it's moving towards the car, not against the car. So this is going to be equal to eight point 75 meters. Actually negative 8.75 minus eight point 75 meters. This is the final positions of the truck and the Order 2.5 the final position of the car. So the distance between the two is just 2.5 plus eight point 75 This is equals to 11 point 25 meters. This is the distance they managed to avoid and the Kalish.

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