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Two cars cover the same distance in a straight line. Car A covers the distance at a constant velocity. Car $\mathrm{B}$ starts from rest and maintains a constant acceleration. Both cars cover a distance of 460 $\mathrm{m}$ in 210 $\mathrm{s}$ . Assume that they are moving in the $+x$ direction. Determine(a) the constant velocity of car A, (b) the final velocity of $\operatorname{car} \mathrm{B},$ and(c) the acceleration of car $\mathrm{B}$ .

2.2$m / s$4.4$m / s$0.021$m / s^{2}$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Simon Fraser University

University of Sheffield

McMaster University

Lectures

04:34

In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

07:57

In mathematics, a position is a point in space. The concept is abstracted from physical space, in which a position is a location given by the coordinates of a point. In physics, the term is used to describe a family of quantities which describe the configuration of a physical system in a given state. The term is also used to describe the set of possible configurations of a system.

01:46

Two cars cover the same di…

04:10

02:03

02:16

2. Two cars cover the same…

02:36

Go Two cars cover the same…

03:34

03:12

Two cars travel at constan…

07:29

Cars $A$ and $B$ travel in…

07:33

Two cars, $A$ and $B,$ tra…

02:49

Two cars travel in the sam…

18:53

Car $A$ is traveling on a …

and this problem. We have two cars. So I'm gonna start by labeling them as Car A and Carby that travel the same distance of 460 meters in the same amount of time. Just 210 seconds. But one car does it with no acceleration and the other car starts from rest and accelerates to complete this task. So that's our set up here. And our goal is to basically find our missing information. We want to figure out how fast car is moving. We want to find out the acceleration of Carby and we also want to figure out the final velocity of car be. So let's start with the easy one here. Since car has no acceleration, its velocity is just equal to its change in position over its change in time, which is 460 divided by 2 10 So the velocity of car eh comes out to be 2.19 meters per second. Okay, so there's our first answer here. We now know the velocity of car, eh? Um Carby, We can actually a car be a couple of different ways. I'm gonna stick to the Kinnah Matic equations because they are right in front of us here. So let's find the velocity of Carby. Um, because we don't know the acceleration we need to use the equation that doesn't have acceleration in it. Which is the X equals 1/2 the plus B not multiplied by T. This comes out to give us 460 equals 1/2 of whatever RV value is multiplied by 2 10 And when I double for 62 9 20 divide by 2 10 we end up with a velocity for carby of 4.38 meters per second. Now I mentioned before there's multiple ways of solving this problem. Um, one thing you'll notice with that velocity is it is exactly double the velocity of car, eh? And there's a trick with Kanna Matics where if two objects air traveling the same distance in the same time, one of which starts from rest and accelerate, someone is going at a constant rate. Um, the starting or the final velocity is always gonna be double the average velocity of the first object. Um and then we're moving into finding the acceleration of Carby, which we really could use any of the equations with a in it. I'm going to use the first equation as that's kind of our most straightforward here. Um and we have 4.38 equal zero plus two 110 multiplied by a divide both sides by 210 and we get an acceleration of 0.2 meters per second squared. It's a very small acceleration, which makes sense because it's a very long period of time and there are three answers. We have the velocity of car, eh? The final velocity of car B and the acceleration of car be as well.

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