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True-False Determine whether the statement is true or false. Explain your answer. Each question refers to a particle in rectilinear motion. If the particle has cons...

Question

True-False Determine whether the statement is true or false. Explain your answer. Each question refers to a particle in rectilinear motion. If the particle has constant acceleration, the velocity versus time graph will be a straight line.

True-False Determine whether the statement is true or false. Explain your answer. Each question refers to a particle in rectilinear motion. If the particle has constant acceleration, the velocity versus time graph will be a straight line.



Answers

True or False The speed of a particle at $t=a$ is given by the value of the velocity at $t=a$ . Justify your answer.

This question asked us to answer tour false. The acceleration of a particle is the second derivative of the position function and to just far answer. We know the first derivative of the position functions velocity and the first derivative of the velocity function is acceleration. There. For the second derivative of possession is acceleration cause we go position velocity acceleration. Therefore, this is true.

They asked us if following his sure falls that the displacement or this particle here is negative and then we want to justify our answer. So it's going to end up being balls and the way we can tell is remember, displacement is going to be the integral of our velocity function over it's time interval. So in this case, it should be zero to buy. We integrate our velocity function, but in this case we don't know what are velocity is. All we have is this area here. So what we could do is come up with the Air Rio from these two sections here because if it's below the ex access, we know it's a negative area. If it's above, we know it's positive area, so we just need to see which one of these has a larger area. So remember, the area of a trapezoid is based one plus base to Rover two times the height, so the height of these would be one. The base here iss, like three point by this one's 1.5, and this upper base looks like it's two, and this one over here looks like it is 1.5 us. Well, so the area of this first base is going to be so to time. Open a part of the height is one. For each of these, That would be two plus three point by supply 3.0.5 times one divided by Tuesday. This is by 0.5, divided by two. Actually, let me right out here. So this is 5.5 divided by two at the this area here to be 1.5 plus 1.5 or three divided by two. So when we would find this, it would be so. That would be 11 force minus three halves, which would give us five force, which is positive, meaning our displacement would be positive and not negative. So this one here would be wants and maybe even be to actually find it all we need to find. Like I was saying, which one of those areas is larger and just from looking at it, we can see that 5.5 over to its larger than three over two

We want to determine whether balling sure false that if the velocity of a particle moving along the X axis is always positive and the displacement is equal to the total distance truck, we want to give a reason as to why so normally, to find total distance trouble. What we would do is integrate on or time interval, absolute value of our velocity function. But since the tea is always bigger than zero, taken absolute value of it, that would be the same as just integrating the velocity function, which in this case there's also just our displacement, so this would be true.

In this problem, we're being asked to evaluate the statement. The velocity of an object represents a change in the objects position. This is false. It's close, but it's false. The velocity of an object represents not just a change in the in the objects position, but it represents a rate of change. So it's determining how fast it's changing, not the fact that it's.


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