Curvilinear Motion: Rectangular Components

Curvilinear motion is a type of motion where a particle or an object moves along a curved path involving changes in direction.

If the object is at point A, its position vector is defined using a fixed frame of reference. Here, the ratio of the position vector with its magnitude represents the unit vector in the direction of the position vector.

As the object moves forward, its position changes with time. The velocity of the object is calculated by taking the time derivative of the position vector. Here, for the fixed frame of reference, the direction of unit vectors does not change with time.

Here, the velocity vector can be expressed using rectangular components, and dividing it with the magnitude of velocity vectors gives the unit vector along the direction of the velocity vector.

Taking the time derivative of the velocity vector gives the acceleration vector for the object in rectangular components.

Dividing the acceleration vector with its magnitude gives the unit vector along the direction of the acceleration vector.