7.3. Rate of Change of Velocity

During uniform motion of an object along a straight line, the velocity remains constant with time. In this case, the change in velocity of the object for any time interval is zero. However, in non-uniform motion, velocity varies with time. It has different values at different instants and at different points of the path. Thus, the change in velocity of the object during any time interval is not zero.

In uniform motion, an object's speed and direction remain steady over time. For example, if a car travels straight at a constant 60 km/h, its velocity does not change; therefore, the change in velocity (final velocity - initial velocity) is zero. In contrast, in non-uniform motion, like a car speeding up in traffic, the velocity alters at different moments. For instance, if the same car speeds up to 80 km/h, the change in velocity has to be noted as 80 km/h - 60 km/h, which is not zero.

Think of riding a bicycle on a straight flat road without pedaling - you're moving uniformly at a constant speed until you hit a hill, and then you either slow down or speed up. The change in your speed can be compared to when you're changing gears on a bicycle—a smooth flat road represents uniform motion while a bumpy terrain illustrates non-uniform motion.

To answer such a question, we have to introduce another physical quantity called acceleration, which is a measure of the change in the velocity of an object per unit time.

Acceleration quantifies how quickly the velocity of an object changes. If you press the gas pedal in a car, you're increasing its speed, causing acceleration. Mathematically, it is calculated using the formula: acceleration = (change in velocity) / (time taken). If a car goes from 20 m/s to 40 m/s in 10 seconds, the acceleration is (40 m/s - 20 m/s) / 10 s = 2 m/s².

Imagine you're riding a seesaw. When two kids push off in opposite directions, they accelerate away from each other. Just like how the seesaw rises quickly from the two pushes, any change in the motion can be described as acceleration.

If the velocity of an object changes from an initial value 'u' to the final value 'v' in time 't', the acceleration 'a' is given by the formula: a = (v - u) / t.

This equation shows how to find acceleration. Simply look at the difference between the final speed (v) and the starting speed (u), then divide by how long it took to make that change (t). If a skateboarder speeds up from 3 m/s to 15 m/s in 4 seconds, their acceleration would be (15 m/s - 3 m/s) / 4 s, which equals 3 m/s².

Consider a roller coaster. When it starts at the top of the hill (low speed) and then drops down, its speed increases rapidly. The increase in speed as it goes down can be directly related to acceleration. The faster it goes, the bigger the force (or acceleration) pulling it downwards.

The acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of velocity. The SI unit of acceleration is m/s².

Acceleration can be classified as positive or negative based on its direction. If a car speeds up while going straight ahead, it's experiencing positive acceleration. Conversely, when a car applies brakes to slow down, it's experiencing negative acceleration (deceleration). This differentiation helps in understanding whether an object's speed is increasing or decreasing.

Think about when you're running and you decide to quicken your pace—that's positive acceleration! But if you see a red light and need to stop, your body experiences negative acceleration as you slow down. These everyday experiences illustrate how acceleration can be both positive and negative.

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