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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.

## 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 $$\tan\beta=\frac{v_B\sin\theta}{v_A-v_B\cos\theta}$$