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Rectilinear Motion

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Kinematics tells about how the motion of particle is. Motion taking a straight line path is what's known as rectilinear motion is!. Its same as the curvilinear motion but does not have the curves or turns in its path. In short its a linear motion whose velocity will be the same in straight line path. Lets see more about this.

Rectilinear Motion of Object
Rectilinear motion of a car

Rectilinear Motion Equations

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A particle starts motion in a straight line from point O having initial velocity u with a constant acceleration a. Let s be the distance traveled by particle to reach point P in time t. At the point where it covers distance s the final velocity is v.
Rectilinear Motion
The Rectilinear motion equations are:
Rectilinear Motion Equations

Rectilinear Motion Problems

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Here are some reference problems on rectilinear motion you can go through it:

Solved Examples

Question 1: A boy moves runs in a race at a distance of 100 m within 40 s. What will be the rectilinear speed?
Solution:
 
Given: Distance traveled d = 100 m, Time taken t = 40 s

The rectilinear speed is given by

v = $\frac{d}{t}$

  = $\frac{100}{40}$

  = 2.5 m/s.
 

Question 2: A particle moves in a straight line has a position given by s = 4t3 - 3t2 + 6. Determine its velocity and acceleration as a function of time.
Solution:
 
Given: The particle motion is given by s = 4t3 - 3t2 + 6

The velocity is given by

V = $\frac{ds}{dt}$

   = $\frac{d(4t^3 - 3t^2 + 6)}{dt}$

   = 12 t2 - 6t + 0

   = 12 t2 - 6t.

The acceleration is given by

a = $\frac{d^2s}{dt^2}$

   = $\frac{d(12 t^2 - 6t)}{dt}$

   = 12 (2t) - 6

   = 24 t - 6.