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Chapter 2: Problem 5

Is it possible to be at position \(x=0\) and still be moving?

Short Answer

Expert verified
Yes, it's possible for an object to be at position \(x=0\) and still be moving.

Step by step solution

01

Understand the Meaning of Position

Position refers to an object's location. The position where \(x=0\) usually signifies the origin or a starting/reference point.
02

Differentiate Position from Motion

Motion refers to the change in position of an object with respect to time. Even if an object is at the position \(x=0\), it could still be moving. The object's position is simply its location at a given point in time.
03

Velocity and Motion

If an object has a velocity other than zero, it means that the object is in the state of motion, regardless of its position. If an object at position \(x=0\) has a non-zero velocity, it implies that the object is moving or about to move, even if it's at the reference point.
04

Answering the Question

So, it's indeed possible for an object to be at position \(x=0\) and still be moving. The object could be passing through \(x=0\) at a given moment, or it could be about to move from rest at \(x=0\), if it has a force applied on it, for instance.

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Most popular questions from this chapter

You can run \(9.0 \mathrm{m} / \mathrm{s}, 20 \%\) faster than your brother. How much head start should you give him in order to have a tie race over \(100 \mathrm{m} ?\)

An X-ray tube gives electrons constant acceleration over a distance of \(15 \mathrm{cm} .\) If their final speed is \(1.2 \times 10^{7} \mathrm{m} / \mathrm{s},\) what are (a) the electrons' acceleration and (b) the time they spend accelerating?

You're atop a building of height \(h,\) and a friend is poised to drop a ball from a window at \(h / 2 .\) Find an expression for the speed at which you should simultaneously throw a ball downward, so the two hit the ground at the same time.

An object's position is given by \(x=b t+c t^{3},\) where \(b=1.50 \mathrm{m} / \mathrm{s}, \quad c=0.640 \mathrm{m} / \mathrm{s}^{3},\) and \(t\) is time in seconds. To study the limiting process leading to the instantaneous velocity, calculate the object's average velocity over time intervals from (a) \(1.00 \mathrm{s}\) to \(3.00 \mathrm{s},\) (b) \(1.50 \mathrm{s}\) to \(2.50 \mathrm{s},\) and \((\mathrm{c}) 1.95 \mathrm{s}\) to \(2.05 \mathrm{s}\) (d) Find the instantaneous velocity as a function of time by differentiating, and compare its value at 2 s with your average velocities.

ThrustSSC, the world's first supersonic car, accelerates from rest to \(1000 \mathrm{km} / \mathrm{h}\) in \(16 \mathrm{s} .\) What's its acceleration?
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