As a car travels 90 meters due north takes center stage, this opening passage beckons readers into a world crafted with expert knowledge, ensuring a reading experience that is both absorbing and distinctly original. The journey begins with a clear understanding of the car’s initial position and orientation, setting the stage for a comprehensive exploration of displacement, distance, velocity, speed, and time.
The discussion delves into the nuances of displacement and distance, highlighting the significance of the northward direction. It then examines the concepts of velocity and speed, exploring the implications of constant velocity. The relationship between distance, velocity, and time is meticulously explained, providing a solid foundation for understanding the car’s motion.
Initial Conditions
The car’s journey begins at a specific point in space. This point is its starting position, which is denoted as the initial position. From this starting point, the car travels in a particular direction, which is known as its initial direction.
Understanding the initial conditions of the car’s motion is crucial because it provides a reference point from which to measure and analyze the car’s subsequent movement.
Starting Position
The car’s starting position is clearly defined and serves as the reference point for its motion. This position is often described using a coordinate system, such as the Cartesian coordinate system, which employs a set of axes to pinpoint a location in space.
Initial Direction
The car’s initial direction indicates the path it takes as it moves from its starting position. This direction is typically expressed in terms of an angle measured relative to a reference axis, such as the positive x-axis in a Cartesian coordinate system.
Displacement and Distance
The car’s displacement is a vector quantity that describes its change in position from its initial point to its final point. Displacement is a directed quantity, meaning it has both magnitude and direction. In this case, the car’s displacement is 90 meters due north.
Distance, on the other hand, is a scalar quantity that describes the total length of the path traveled by the car. Distance is not a directed quantity, so it does not have a direction. In this case, the car’s distance traveled is also 90 meters.
Significance of the Northward Direction
The northward direction of the car’s displacement is significant because it indicates the direction in which the car moved. Without the northward direction, we would only know the magnitude of the car’s displacement, but we would not know in which direction it moved.
Velocity and Speed
Now that we have established the initial conditions, displacement, and distance, let’s delve into the concepts of velocity and speed.
Velocity, A car travels 90 meters due north
Velocity measures the rate of change in an object’s position over time, taking into account both speed and direction. It is a vector quantity, meaning it has both magnitude (speed) and direction.
The formula for velocity is:
v = Δd / Δt
where:
- v is velocity
- Δd is the change in displacement
- Δt is the change in time
Speed
Speed, on the other hand, is a scalar quantity that measures the rate at which an object travels, regardless of direction. It is simply the magnitude of velocity.
The formula for speed is:
s = Δd / Δt
where:
- s is speed
- Δd is the change in distance
- Δt is the change in time
Constant Velocity
An object with constant velocity is moving at a steady rate and in a straight line. Its speed and direction do not change over time.
In our case, since the car is traveling 90 meters due north, its velocity is constant. Its speed is 90 meters per second, and its direction is north.
Time and Motion
Now that we know the distance traveled by the car, let’s explore the relationship between distance, velocity, and time.
Calculating Time
To calculate the time taken for the car to travel 90 meters, we can use the formula:
Distance = Velocity x Time
Rearranging the formula to solve for time, we get:
Time = Distance / Velocity
Substituting the given values, we get:
Time = 90 meters / 15 meters per second
Time = 6 seconds
Therefore, the car took 6 seconds to travel 90 meters.
Motion of the Car
The motion of the car can be summarized as follows:
- Initial position: 0 meters
- Final position: 90 meters
- Distance traveled: 90 meters
- Velocity: 15 meters per second
- Time taken: 6 seconds
Coordinate System and Graphing
To accurately represent the car’s motion, we establish a coordinate system with the origin at the car’s initial position. The positive x-axis points north, aligning with the direction of the car’s travel.
Establishing a Coordinate System
The coordinate system provides a framework for tracking the car’s displacement. The x-coordinate of the car represents its distance north of the origin, and its y-coordinate represents its distance east or west of the origin (which is assumed to be zero since the car is traveling due north).
Creating a Graph of Displacement vs. Time
A graph of the car’s displacement over time provides a visual representation of its motion. The x-axis of the graph represents time, while the y-axis represents the car’s displacement north of the origin.
Significance of the Graph’s Slope and Intercepts
The slope of the graph represents the car’s velocity, which is the rate at which its displacement changes over time. A positive slope indicates that the car is moving northward, while a negative slope indicates southward motion. The y-intercept of the graph represents the car’s initial displacement, which is zero in this case since the car starts from the origin.
Applications and Examples
The principles of uniform motion in a straight line find numerous applications in real-world scenarios. Understanding these concepts enables us to analyze and predict motion in various situations.
One practical application lies in determining the travel time and distance for vehicles. By knowing the constant speed of a car and the distance it needs to cover, we can estimate the time it will take to reach its destination.
This knowledge is crucial for planning efficient journeys and avoiding delays.
Engineering and Design
In engineering and design, understanding uniform motion is essential for designing efficient transportation systems. Engineers consider the speed and distance traveled by vehicles to optimize road layouts, traffic flow, and safety measures.
Projectile Motion
The principles of uniform motion also play a role in projectile motion. When an object is launched with an initial velocity, it travels in a parabolic path under the influence of gravity. By understanding the constant horizontal velocity and the vertical motion due to gravity, we can calculate the trajectory and landing point of the projectile.
Problem Design
Design an experiment to demonstrate the principles of uniform motion in a straight line:
- Set up a track with a known distance, such as 100 meters.
- Use a toy car or other object that can move at a constant speed.
- Measure the time it takes for the object to travel the distance.
- Calculate the object’s speed using the formula: speed = distance/time.
- Repeat the experiment several times to ensure accuracy.
By conducting this experiment, students can observe firsthand the relationship between distance, time, and speed, and gain a practical understanding of uniform motion.
Questions Often Asked: A Car Travels 90 Meters Due North
What is the difference between displacement and distance?
Displacement refers to the change in position of an object from its starting point, while distance refers to the total length of the path traveled.
What is the significance of the northward direction in this scenario?
The northward direction indicates that the car is moving in a straight line directly towards the north.
How is velocity different from speed?
Velocity takes into account both the speed and direction of an object’s motion, while speed only measures the rate at which an object is moving.
