91Ó°ÊÓ

Understanding uniform acceleration is key to solving kinematics problems like the one in our exercise. When an object accelerates uniformly, it means that the rate of change of its velocity is constant throughout its motion. This concept simplifies calculations since the acceleration value remains unchanged over time.

In the case of our truck and car problem, both the car and the truck start from rest, implying their initial velocity is zero. They accelerate at different constant rates of 2.10 m/s two for the truck and 3.40 m/s two for the car. This constant acceleration means we can reliably apply kinematic equations to predict their future positions and velocities based on time elapsed.

Uniform acceleration also allows us to use straightforward formulas, like the equations of motion and velocity-time graphs, to understand and solve the problem effectively.

The equations of motion are essential tools when dealing with problems involving uniform acceleration. These equations help relate the motion characteristics of an object, like displacement, time, initial velocity, and acceleration.

In our exercise, we apply one of the most fundamental equations of motion: \[ x = ut + \frac{1}{2} a t^2 \] Where:

• \( x \) is the displacement
• \( u \) is the initial velocity, which is zero for both the car and the truck
• \( a \) is the constant acceleration
• \( t \) is the time elapsed

For the truck, substituting into this equation allows us to find the time it takes to travel 60 meters. Similarly, for the car, this equation helps determine its position relative to the truck's position when both vehicles are side by side.

We also used the equation \( v = u + at \) to calculate the velocities of the car and truck afterward, which tells us how fast each was moving at the point of overtaking.

A velocity-time graph is a powerful visual tool that allows us to understand how the velocity of an object changes over time. It provides insights into the nature of an object's motion, especially when dealing with uniformly accelerated motion.

For objects with constant acceleration, like our car and truck, the velocity-time graph is a straight line. The slope of this line represents the acceleration. In this scenario, a steeper slope indicates a higher acceleration, which is why the car's line is steeper than the truck's.

The area under the velocity-time graph gives the displacement. For our problem, this information helps verify the calculations made using equations of motion. In essence, plotting these graphs for both vehicles, we can see how each progresses over time and pinpoint the moment they are side by side, reinforcing the algebraic solution with a visual check.