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Theory Explanation of Numerical 2.5

In Numerical 2.5, an object is moving with uniform (constant) acceleration.
You are told how its speed changes over a certain period of time, and you are usually asked to find how far it travels during this motion.

✔ What physical situation does the numerical describe?

The object begins moving with some speed (sometimes from rest, sometimes from a given velocity).

Its speed keeps increasing at a steady rate, which means the acceleration is the same at every moment.

Because the speed keeps rising evenly, the object covers greater and greater distances in each following second.

✔ What is the key concept?

This numerical helps explain how an object behaves when it is under uniform acceleration, such as:

A car increasing its speed smoothly,

A ball rolling down a slope,

Any body whose velocity rises evenly with time.

When the velocity increases regularly, the distance covered also changes in a predictable way.

✔ Why does the object cover more distance over time?

At the beginning:

The object is moving slowly, so it covers only a small distance in each second.

As time passes:

Its speed becomes higher, so it covers more distance in each second.

This gradual increase in distance covered is a natural result of the object’s steadily increasing speed.

✔ What are we asked to find in this numerical?

You are usually asked to determine the total distance traveled while the object is speeding up.

This is done by understanding:

How the velocity changes from the start to the end,

How long the object continues to accelerate,

How increasing speed affects the distance covered.

✔ Why do we study such situations?

This numerical teaches important ideas about motion:

Objects do not cover equal distances when their speed is changing.

When the speed increases uniformly, the total distance can be predicted.

Many real-life motions—cars accelerating, falling objects (ignoring air resistance), rolling objects—behave in this way.