EQUATIONS FOR LINEAR UNIFORMLY ACCELERATED MOTION

Introduction to uniformly accelerated linear motion

The velocity of the body is never uniform for whole the time of motion. The velocity of the body increases and decreases randomly. Since the velocity of the body keeps on changing, it is said to have an acceleration. The time rate of the change of the velocity of the body is called the acceleration. Thus, the acceleration is the change in the velocity in each unit of time. In the case when the change in velocity in each unit of time is constant, then the body has the uniform acceleration and such motion is called the uniformly accelerated linear motion. If the change in velocity in each unit of time is not constant, the body is said to be moving with variable acceleration and such motion is called the non uniformly accelerated motion. In general, we can say that the motion of a vehicle on the road is non uniformly accelerated as its velocity increases or decreases randomly. Here we study about the uniformly accelerated linear motion.

Equations in Uniformly Accelerated Linear Motion

A motion, in which change in velocity in each unit of time is constant, is called the uniformly accelerated linear motion. There are three equations of motions, which are used, in the uniformly accelerated linear motion. The equations are as follows:

(i) v = u + at

(ii) s = ut + ½ at²

(iii) v² = u² + 2as

Where u is the initial velocity of the moving body, v is the final velocity of the moving body, s is the distance covered by the moving body, t is the time taken by the moving body, a is the acceleration of the body.

Graphs for the Uniformly Accelerated Linear Motion

The velocity time graph for the uniformly accelerated linear motion is a straight line as shown below.


Thus from the discussion we found the uniformly accelerated linear motion and knew about its nature.

 Here when the body has positive constant acceleration, the slope of the graph is upwards. In case, the body has negative constant acceleration, the slope of the graph id downwards.