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 a car |

A particle starts motion in a straight line from point

The Rectilinear motion equations are:

**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**.**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 = 4t

^{3}- 3t

^{2 }+ 6. Determine its velocity and acceleration as a function of time.

**Solution:**

Given: The particle motion is given by s = 4t

^{3}- 3t

^{2}+ 6

The velocity is given by

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

= $\frac{d(4t^3 - 3t^2 + 6)}{dt}$

= 12 t

^{2}- 6t + 0

= 12 t

^{2}- 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.