Please explain the first question in solved examples of kinematics

In kinematics, the first question often revolves around understanding the basic concepts of motion, such as displacement, velocity, and acceleration. Let's break this down using a common example that illustrates these concepts clearly.

Understanding Motion Through an Example

Imagine a car that starts from rest and accelerates uniformly. For instance, let's say the car accelerates at a rate of 2 meters per second squared (m/s²) for a duration of 5 seconds. We want to find out how far the car travels during this time and what its final velocity is.

Step 1: Identify the Known Values

• Initial Velocity (u): 0 m/s (since the car starts from rest)
• Acceleration (a): 2 m/s²
• Time (t): 5 seconds

Step 2: Calculate Final Velocity

To find the final velocity (v) of the car, we can use the formula:

v = u + at

Substituting the known values:

v = 0 m/s + (2 m/s² * 5 s) = 10 m/s

So, the final velocity of the car after 5 seconds is 10 m/s.

Step 3: Calculate Displacement

Next, we need to determine how far the car has traveled during this time. The formula for displacement (s) when starting from rest is:

s = ut + (1/2)at²

Again, substituting the known values:

s = (0 m/s * 5 s) + (1/2 * 2 m/s² * (5 s)²)

This simplifies to:

s = 0 + (1/2 * 2 * 25) = 25 meters

Thus, the car travels a distance of 25 meters in 5 seconds.

Summary of the Example

In this scenario, we learned that:

• The car's final velocity after 5 seconds is 10 m/s.
• The total distance traveled by the car is 25 meters.

This example illustrates the fundamental principles of kinematics, showing how to apply equations of motion to solve problems involving uniform acceleration. By breaking down the problem into manageable steps, we can clearly see how each component contributes to the overall motion of the car.