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Triple Choice An object's position-time graph is a straight line with a negative slope. Is the speed of this object positive, negative, or zero? Explain.

Short Answer

Expert verified
The object's speed is positive.

Step by step solution

01

Understanding Slope in Position-Time Graphs

In a position-time graph, the slope of the line indicates the velocity of the object. A positive slope indicates positive velocity, a negative slope indicates negative velocity, and a zero slope indicates zero velocity.
02

Identifying the Slope

The problem states that the position-time graph is a straight line with a negative slope. This indicates that the object is moving in the opposite direction from that defined as positive, hence the velocity is negative.
03

Relating Slope to Speed

Speed is the absolute value of velocity. Even though the velocity is negative due to the negative slope, speed, being a scalar, is always positive or zero. The speed is the magnitude of velocity.
04

Conclusion on Speed

Since the velocity is negative, the speed is the positive magnitude of that velocity. Therefore, the object's speed is positive.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Velocity
Velocity is a fundamental concept in physics and is crucial for understanding motion. It describes the rate of change of an object's position with respect to time and is directional. This means velocity is a vector quantity, having both magnitude and direction. For instance, if a car moves at 60 km/h to the east, its velocity is described by both its speed (60 km/h) and its direction (east).

Velocity can be positive or negative, depending on direction:
  • Positive velocity indicates movement in the defined positive direction.
  • Negative velocity indicates movement in the opposite direction.
Understanding velocity is key when analyzing position-time graphs. The slope of the line on such a graph represents the object's velocity.
Negative Slope
When analyzing position-time graphs, a negative slope indicates important information about the object's motion. The slope is the ratio of change in position over change in time. Therefore, a negative slope suggests a decrease in position as time increases, which implies backward motion relative to the defined direction.

A position-time graph with a negative slope shows the object is moving in the opposite direction:
  • The steeper the slope, the greater the magnitude of the velocity.
  • If the slope is not steep, the velocity is smaller in magnitude.
In essence, a negative slope in these graphs translates directly to negative velocity.
Speed
Speed is a measure of how fast an object is moving without considering the direction. It is the magnitude of velocity and is always a positive value (or zero if there is no motion). Since speed does not account for direction, it is known as a scalar quantity.

Here are key aspects of speed:
  • Speed is calculated as the absolute value of velocity.
  • It cannot be negative, only zero or a positive number.
In the context of a position-time graph, regardless of whether the slope is positive or negative, the speed remains positive because it represents the magnitude of motion.
Scalar Quantity
Scalar quantities are simple and easy to grasp as they have only magnitude and no direction. Unlike vectors, scalars do not indicate where the object is headed. They just reflect how much.

Common examples of scalar quantities include:
  • Speed (magnitude of velocity)
  • Distance (total path covered)
  • Time
  • Mass
Understanding scalar quantities helps in differentiating from vectors, like velocity, that encapsulate direction and magnitude. Scalars simplify calculations when direction is inconsequential, like determining how fast a car travels without caring in which direction.

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Most popular questions from this chapter

Consider a rabbit that is at \(x=8.1 \mathrm{~m}\) at \(t=0\) and moves with a constant velocity of \(-1.6 \mathrm{~m} / \mathrm{s}\). What is the equation of motion for the rabbit?

Two people walking on a sidewalk have the following equations of motion: $$ \begin{aligned} &x_{1}=8.2 \mathrm{~m}+(-1.1 \mathrm{~m} / \mathrm{s}) t \\ &x_{2}=5.9 \mathrm{~m}+(1.7 \mathrm{~m} / \mathrm{s}) t \end{aligned} $$ (a) Which person is moving faster? (b) Which person will be at \(x=0\) at some time in the future?

The initial position of an object that moves with constant velocity is increased. Does this change the intercept or the slope of the position-time graph of the object's motion? Explain.

The position-time equation of motion for a bunny hopping across a yard is $$ x_{\mathrm{f}}=8.3 \mathrm{~m}+(2.2 \mathrm{~m} / \mathrm{s}) t $$ (a) What is the initial position of the bunny? (b) What is the bunny's velocity? 36\. A bowling ball moves with constant velocity from an initial position of \(1.6 \mathrm{~m}\) to a final position of \(7.8 \mathrm{~m}\) in \(3.1 \mathrm{~s}\). (a) What is the position-time equation for the bowling ball? (b) At what time is the ball at the position \(8.6 \mathrm{~m}\) ?

Triple Choice The position-time graph for the motion of a certain particle is a smooth curve, like a parabola. At a given instant of time, the tangent line to the positiontime graph has a negative slope. Is the instantaneous velocity of the particle at this time positive, negative, or zero? Explain.

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