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  • Understanding Motion with Constant Velocity and Acceleration
    If a moving body's velocity and acceleration are always directed along its path, the path must be a straight line. Here's why:

    * Velocity: Velocity describes the rate and direction of motion. If the velocity is always directed along the path, the body is always moving in the same direction.

    * Acceleration: Acceleration is the rate of change of velocity. If the acceleration is always directed along the path, it means the body is either speeding up or slowing down in the same direction it's already moving.

    Example: Imagine a car driving down a straight road. Its velocity is always in the direction of the road, and if it accelerates (speeds up or slows down), the acceleration is also along the road.

    Why not a curved path?

    If the path were curved, the velocity would have to change direction to follow the curve. This means the acceleration would have a component perpendicular to the path, causing the body to deviate from its straight-line trajectory.

    In summary: A body's velocity and acceleration always directed along its path signifies a linear (straight-line) movement.

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