Motion in One Dimension

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Physics Newtonian Mechanics Motion in One Dimension

	Position , Velocity , and Acceleration Vectors:
	The position of an object is specified by the co-ordinates. When an object is in plane and has a position vector r in a rectangular co-ordinate system then the position vector can be denoted as: When the object changes its position (from r₁ to r2 in terms of position vectors) then its displacement is given by, r₂ – r₁ = Δr. The displacement is a vector quantity and obeys all the properties of vectors. Now the average velocity can be defined as the displacement over time interval: When the time interval is very small so that it is near to zero, the instantaneous velocity of the object along x-axis would be the rate of change of displacement: Now the average acceleration is given by the change in velocity over time interval: The instantaneous acceleration is the acceleration of an object at a particular instant of time and is defined as the rate of change of velocity: It is worth noting that the velocity and acceleration are vector quantities, and we are now using them in one dimension. It can also be noted that the instantaneous velocity is the slope of the position ~ time graph and instantaneous acceleration is the slope of velocity ~ time graph.