Equations of Motion-Physics Class 11

Equations of Motion

The Equations of Motion in a Straight Line Are:

\(\begin{array}{l}v=u+at\end{array} \) \(\begin{array}{l}s=ut+\frac{1}{2}at^{2}\end{array} \) \(\begin{array}{l}v^2=u^2+2as\end{array} \)

Where,

  • v = final velocity of the particle
  • u = initial velocity of the particle
  • s = displacement of the particle
  • a = acceleration of the particle
  • t = time interval in which the particle is in consideration

In a plane, we have to apply the same equations separately in both the directions: Y axis and Y-axis.

This would give us the equations for motion in a plane:

\(\begin{array}{l}v_y=u_y+a_yt\end{array} \) \(\begin{array}{l}s_y=u_yt+\frac{1}{2}a_yt^{2}\end{array} \) \(\begin{array}{l}v_y^2=u_y^2+2a_ys\end{array} \)

Where,

  • vy= final velocity of the particle in y direction
  • uy= initial velocity of the particle in y direction
  • sy= displacement of the particle in y direction
  • ay= acceleration of the particle in y direction
  • t = time interval in which the particle is in consideration

Similarly, for X-axis:

\(\begin{array}{l}V_x=u_x+a_xt\end{array} \) \(\begin{array}{l}S_x=u_xt+\frac{1}{2}a_x t^{2}\end{array} \) \(\begin{array}{l}V_x^2=u_x^2+2a_x s\end{array} \)

Where,

  • vx= final velocity of the particle in x direction
  • ux= initial velocity of the particle in x direction
  • sx= displacement of the particle in x direction
  • ax= acceleration of the particle in x direction
  • t = time interval in which the particle is in consideration

Relative Motion

When we say the motion of body A relative to B we mean motion of A, as observed from B’s frame of reference. Mathematically it is represented as:

\(\begin{array}{l}V_{BA}~=~V_B~–~V_A\end{array} \)

Where,

  • VBA = Velocity of B as observed from A.
  • VB = Velocity of B from the earth as the reference frame.
  • VA = Velocity of A from the earth as the reference frame.

Consider a man running uphill while it is raining. It is difficult to decide from which side the man will get wet if we do not know the relative m of the man and rain with respect to each other. Suppose the components of velocity of man are given as 6i + j and that of rain is given by 3i – 3j. If we can find the angle at which the rain hits the man, we can easily decide from which direction the man gets hit by the rain. To find the relative velocity or relative motion of rain with respect to man, the velocity of a man with respect to rain must be subtracted, i.e.,

\(\begin{array}{l}\overrightarrow{v_{r|m}}~ =~\overrightarrow{v_{r}} ~-~\overrightarrow{v_{m}}\end{array} \)

Relative motion can be explained using the vector representation as:

Where,

It can be seen that with respect to the man, the rain is falling at an angle of

\(\begin{array}{l}tan^{-1} \left( \frac 34 \right)\end{array} \)

. So, if the man is running in positive X- direction then rain must hit him from the front direction. So, if the man has to wear a bag, he must wear it on his back to prevent it from rain. Thus only by knowing the velocities, the direction of hitting of rain can be determined. Now, what happens if the horizontal component of the velocity of rain and man becomes equal? Interesting, isn’t it? Well, in such a situation the rain will not hit the man from either side. So, to answer the question of whether one should run fast or slow in the rain to get less wet, it all depends on the velocities or relative motion.

in X-axis and Y-axis to find the unknown parameters.

Frequently Asked Questions on Motion In A Plane

Q1

What is motion in a plane?

Motion in a plane means motion in a two-dimensional plane which includes x-axis and y-axis.

Q2

What is one-dimensional motion and two-dimensional motion?

When the object travels in a straight line, irrespective of the direction is known as one-dimensional motion. When the object travels in x and y coordinates with a constant velocity, it is known as two-dimensional motion.

Q3

What is accelerated motion?

When the velocity is increased gradually with respect to the time, it is known as accelerated motion.

Q4

What is oscillatory motion?

The to and fro motion of the object about its mean position is known as oscillatory motion.

Q5

What is projectile motion?

Projectile motion is when the object is projected into air and gravity is the only force acting upon the object.

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.