Question

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

The object's speed is positive.

Step-by-step solution

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.

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.

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.

Conclusion on Speed

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

Key concepts

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.