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Motion in a straight line formulas

On this page find all the formulas you need to remember for motion in a straight line. These are the important formulas if you are in class 11 or preparing for NEET, JEE-Mains or JEE-Advanced.
I will attach a downloadable PDF file of this article so that you can print it out for your preparation and studies.


Motion in a straight line class 11 formulas

  • Distance – The total length that is travelled between different positions.
  • Displacement – Distance between two points in a particular direction.
    • Formula :- $\Delta x= x_f-x_i$
    • $\Delta x \rightarrow$ Displacement
    • $x_f\rightarrow$ final position
    • $x_i\rightarrow$ initial position
  • Speed – the total distance covered divided by the time taken to cover that distance.
    • Formula :- $\text{Speed}=\frac{\text{Total Distance Covered}}{\text{Time Taken}}$
    • Unit – $m/s$, $Km/hr$ or $mph$(mile per hour)
    • Dimensions – $[M^0LT^{-1}]$
  • Velocity – the displacement divided by the time it takes for the displacement
    • Formula :- $Velocity=\frac{Displacement}{Time}$
    • Unit – $m/s$, $Km/hr$ or $mph$(mile per hour)
    • Dimensions – $[M^0LT^{-1}]$
  • Average Speed – the total distance covered divided by the time taken to cover that distance
    • Formula :- $\text{Average Speed}=\frac{\text{Total Distance Covered}}{\text{Time Taken}}=\frac{\Delta x}{\Delta t}$
    • Body covering different distances with different speeds $$\bar v=\frac{s_1+s_2+s_3+….}{t_1+t_2+t_3+….}=\frac{s_1+s_2+s_3+….}{\frac{s_1}{v_1}+\frac{s_2}{v_2}+\frac{s_3}{v_3}+…..}$$
    • If the body covers the first half of the total distance with speed $v_1$ and the second half with the speed $v_2$, then the average speed is given by $$\bar v=\frac{2v_1v_2}{v_1+v_2}$$
      In this case, the average speed is the harmonic mean of individual speeds.
    • Body is moving with different speeds in different time intervals then Total distance travelled $=v_1t_1+v_2t_2+v_3t_3+….=$ Total time taken $=t_1+t_2+t_3+….$ $$\bar v= \frac{v_1t_1+v_2t_2+v_3t_3+….}{t_1+t_2+t_3+….}$$
      • If $t_1=t_2=t_3=….=t_n=t$ then, $$\bar v=\frac{(v_1+v_2+v_3+….)t}{nt}=\frac{(v_1+v_2+v_3+….)}{n}$$
        • In this case, the average speed is the arithmetic mean of the individual speeds.
  • Average Velocity – the total displacement covered divided by the time taken for that displacement
    • Formula :- $\text{Average Velocity}=\frac{\text{Displacement}}{\text{Time Taken}} \,\,\,\,\,\,or,\,\,\,\,\, \bar v=\frac{\Delta \vec x}{\Delta t}$
    • Finding position from velocity – $x = x_{0} + \bar{v} t$
  • Instantaneous Velocity – is defined as the velocity of an object at a particular instant of time.
    • Formula :- $v(t) = \frac{dx(t)}{dt}$
  • Instantaneous Speed – is defined as the speed of an object at a particular instant of time. It is the absolute value of instantaneous velocity.
    • Formula :- $\text{Instantaneous speed} = |v(t)|$
  • Acceleration – The rate of change of velocity is called acceleration.
    • Formula :- $a=\frac{\Delta \vec{v}}{\Delta t}=\frac{v_f-v_i}{t_f-t_i}$
  • Instantaneous acceleration – acceleration of a particle at a particular instant of time
    • Formula :- $a=\lim_{\Delta\rightarrow0}\frac{\Delta v}{\Delta t}=\frac{dv}{dt}$
  • Equations of motion with constant acceleration
    • First Equation of motion – finding velocity from acceleration – $v=v_0+at$
    • Second Equation of motion – finding position from velocity and acceleration – $x = x_{0} + v_{0} t + \frac{1}{2} at^{2}$
    • Third Equation of motion – finding velocity from distance and acceleration – $v^{2} = v_{0}^{2} + 2a(x – x_{0})$
    • Equation for finding distance travelled in $n^{th}$ second of object’s journey – $S_n=u+a(n-\frac{1}{2})$
  • Motion under gravity
    • Equations of motion for a freely falling body
      • $v=u+gt$
      • $s=ut+\frac{1}{2}gt^2$
      • $v^2-u^2=2gs$
    • For a body falling freely under the action of gravity, $g$ is taken as positive.
    • For the body thrown vertically upwards, $g$ is taken as negative.
    • When the body is just dropped, $u=0$
    • For a body thrown vertically up with initial velocity $u$
    • Maximum height reached is, $h=\frac{u^2}{2g}$
    • time of ascent = time of descent $=\frac{u}{g}$
    • total time of flight $=\frac{2u}{g}$
    • the velocity of fall at the point of projection $=u$
    • velocity attained by a body dropped from height $h$, $v=\sqrt{2gh}$
  • Relative Velocity
    • Relative velocity of object $A$ w.r.t. object $B$ is, $v_{AB}=v_A-v_B$
    • When two objects are moving in the same direction, $v_{AB}=v_A-v_B$
    • When two objects are moving in opposite directions, $v_{AB}=v_A+v_B$
    • When $v_A$ and $V_B$ are inclined to each other at an angle $\theta$ $$\vec{v}_{AB}=\sqrt{v_A^2+v_B^2-2v_Av_B\cos\theta}$$
    • If $v_{AB}$ makes an angle $\beta$ with $v_A$, then $$\tan\beta=\frac{v_B\sin\theta}{v_A-v_B\cos\theta}$$

Rectilinear Motion Formula PDF File Download

Download this free Motion in a straight line formula for neet, class 11 and jee as a pdf. Learn more about what is Rectilinear Motion in physics.