## Variable Speed and Velocity – Class 11 | Chapter – 3 | Physics Short Notes Series PDF for NEET & JEE

Variable Speed and Velocity: Variable speed and velocity refer to situations where an object’s speed or velocity changes over time. In these cases, the object’s motion is not uniform, and its speed and/or direction of motion can vary.

• Variable Speed: When an object’s speed changes over time, it is said to have variable speed. For example, a car moving through a city may have a variable speed due to traffic lights, intersections, and other factors that affect its rate of motion. The car may speed up, slow down, or come to a complete stop depending on these factors. Variable speed is typically measured in distance per time (e.g., meters per second or kilometers per hour) and may be represented graphically using a speed-time graph.
• Variable Velocity: When an object’s velocity changes over time, it is said to have variable velocity. Velocity includes both the object’s speed and direction of motion, so a change in velocity can involve a change in either or both of these factors. For example, a car moving around a curve in a road may have a variable velocity because its direction of motion is changing. Variable velocity is typically measured in distance per time and direction (e.g., 30 meters per second eastward) and may be represented graphically using a velocity-time graph.

## Difference between Variable Speed and Velocity

Variable speed and velocity are related concepts, but they are not the same. The main difference between variable speed and velocity is that variable speed refers to changes in the rate at which an object travels without regard to its direction, while velocity includes both the speed of an object and its direction of travel.

Here are some additional differences between variable speed and velocity:

• Scalar vs Vector Quantity: Variable speed is a scalar quantity that only has a magnitude (i.e., a numerical value) and is measured in distance per time. Velocity, on the other hand, is a vector quantity that has both magnitude (i.e., speed) and direction and is measured in distance per time and direction.
• Constant vs. Changing Direction: An object moving at a variable speed may have a constant or changing direction, but its speed is changing over time. In contrast, velocity takes into account both the rate and direction of motion, so if an object changes its direction, its velocity changes even if its speed remains constant.
• Displacement vs Distance: Variable speed is related to the distance traveled by an object over a given period of time, while velocity is related to the displacement of an object over a given period of time. Displacement is the shortest distance between the starting and ending points, while distance is the total length of the path taken by the object.

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