Motion in Straight Line

Motion in Straight Line:

Motion in straight line is defined as motion in one dimension (1-D). It is also known as linear motion. It can be participated in two parts -

(i) uniform linear motion and 

(ii) non-uniform linear motion

Uniform Linear Motion:

In this motion a body covers equal distance in equal time intervals i.e. velocity along the path is constant. In this motion a body moves with a constant acceleration. 

Non-uniform Linear Motion:

In this motion a body moves with a variable velocity in a given interval of time.

Equation of Motion with constant Acceleration:

Consider that a particle has constant acceleration 'a'. It's initial velocity is 'u' and final velocity is 'v' after 't' time. Now acceleration can be written as: dv/dt = a  

Particle covers 's' distance or displacement (since particle is moving along the straight line) in time 't'. From 1st equation-

write equation 1st again-

Displacement of Particle in nth second:

From 2nd equation-

Example 1: A car started from rest and moves with a constant acceleration 2m/s². Find the following-

(i) velocity of the car after 4s  ?

(ii) total distance covered by the car in 8s ?

(iii) what is the displacement of the car if it's displacement is 36m

Example 2: A particle has constant acceleration 0.5 m/s². Find its displacement in 5th and 8th second ?

Free Fall:

Free fall is the most common example of the motion in straight line. A free falling object is an object that is falling under the influence of gravity. Gravitational acceleration is defined as 'g' and its value (9.8 m/s²) is taken as constant near the surface of the earth. We take vertically upward as positive direction, then if a particle, which has initial velocity u and final velocity is v, is falling from any height then motion of equations can be transferred as -

Example 3: A ball is thrown up with a initial velocity 5 m/s². Find maximum height attained by the ball ? (take g = 10 m/s²)