This article delves into analyzing truck motion using velocity-time graphs, a crucial tool for studying and describing uniformly varied rectilinear motion. We will solve a typical Physics 10 problem together, gaining a deeper understanding of how to interpret and apply these graphs in real-world scenarios, particularly within the truck transportation sector.
Analyzing Truck Motion Problem on Highway
Problem: A truck is moving at a constant velocity on a highway for a duration of Δt. When the driver notices a sign indicating a hazardous area prone to accidents, they decide to decelerate. After a period of Δt1, the driver unexpectedly spots an accident ahead and applies the brakes sharply to stop the truck within a short time Δt2, in order to avoid a collision. Assume the truck travels on an empty stretch of road throughout this process.
Requirements:
a. Draw a velocity-time graph representing the truck’s motion process.
b. In which phase is the slope of the graph the steepest?
Detailed Solution and Analysis of Velocity-Time Graph
a. Drawing the Velocity-Time Graph
To draw the velocity-time graph, we need to break down the truck’s motion into distinct phases:
- Phase 1: Uniform Rectilinear Motion. During the initial time interval Δt, the truck moves at a constant velocity. On the velocity-time graph, this phase is represented by a horizontal straight line, parallel to the time axis.
- Phase 2: Deceleration (Uniformly Decelerated Motion). Upon seeing the hazard sign, the driver begins to decelerate for a time interval Δt1. This is a phase of uniformly decelerated motion with negative acceleration (acceleration opposite to the direction of velocity). On the graph, this phase is a downward sloping straight line. The slope of this line represents the magnitude of the deceleration.
- Phase 3: Hard Braking (Uniformly Decelerated Motion with High Acceleration). When an accident is spotted, the driver brakes hard for a short time interval Δt2 to come to a complete stop. This is also a phase of uniformly decelerated motion, but with a much larger negative acceleration compared to phase 2, allowing the truck to stop quickly. On the graph, this phase is a very steeply downward sloping line, almost vertical.
Below is the velocity-time graph illustrating the truck’s motion process:
Velocity-time graph illustrating truck motion in three phases: constant speed, deceleration, and hard braking.
b. Steepest Slope on the Graph
The slope of the velocity-time graph represents the acceleration of the motion. The steeper the slope, the greater the acceleration. In this problem, the steepest slope of the graph occurs in Phase 3: hard braking (Δt2).
Explanation:
- Phase 1 (uniform motion): The slope is 0 because the velocity is constant, and the acceleration is 0.
- Phase 2 (deceleration): The slope has a negative value but is small (gradual deceleration).
- Phase 3 (hard braking): The slope has a negative and very large value (rapid deceleration to stop the vehicle).
Therefore, the steepest slope on the velocity-time graph represents the phase where the truck decelerates most rapidly, which is when the driver brakes hard to avoid an accident. This highlights the importance of safe braking, especially for cargo trucks, to ensure traffic safety and protect goods.
Real-World Application and Optimizing Truck Operation
Analyzing velocity-time graphs is not only helpful for theoretical understanding but also has practical applications in truck operation. For transportation businesses like Xe Tải Mỹ Đình, grasping the physics principles of motion and acceleration can assist in:
- Driver Training: Helping drivers better understand the processes of acceleration, deceleration, and braking, leading to safer and more efficient driving.
- Fuel Optimization: Understanding uniform motion and uniformly varied motion enables drivers to adjust speed appropriately, avoiding hard braking and sudden acceleration, thus saving fuel.
- Ensuring Cargo Safety: Smooth driving, avoiding hard braking, also helps protect cargo, especially fragile goods, during transportation.
Although the problem above doesn’t directly mention “a truck carrying 3 trips“, it serves as a fundamental illustration of truck motion. In reality, operating “a truck carrying 3 trips” or more still adheres to the same physics principles of motion. Understanding these principles is the foundation for operating trucks safely, efficiently, and optimizing costs.
