Scalars vs. Vectors
A scalar quantity has only magnitude.| A vector quantity has both magnitude and direction.| Scalars can be added, subtracted, multiplied and divided just as ordinary numbers, i.e., scalars are subjected to simple arithmetic operations.| Vectors cannot be added, subtracted and multiplied following simple arithmetic laws. Arithmetic division of vectors is not possible at all.| Example: mass, volume, time, distance, speed, work, temperature| Example: displacement, velocity, acceleration, force| Distance and displacement
Distance is defined as the ground covered by a moving object during its motion. Its SI unit is metre (m). It has only magnitude, but no direction. Distance can never be negative. The minimum value of distance is zero. Displacement is defined as how far an object has moved relative to the starting point. Its SI unit is metre (m). It has both magnitude and direction. Displacement can be positive, negative, or zero. Speed and Velocity
Speed is a physical quantity that enables us to know how the position of an object changes with time, i.e. speed gives us an idea about the slowness and fastness of a moving object. It is obtained by dividing the distance travelled by a body by the total time taken to cover that distance. speed =
where, s = speed of the moving object
d= distance travelled by the object
t = time taken to cover distance s
The SI unit of speed is m/s.
The speed of an object tells about its fastness or slowness. It does not give us any idea about the direction of its motion. The physical quantity that gives the speed of a moving object with its direction of motion is called velocity. The velocity v of a moving object is given by the ratio of distance d travelled in a given direction, i.e., the displacement with the time taken t. ∴Velocity =
Magnitude of velocity,
Acceleration---The rate of change of velocity of a moving object is called acceleration. An...