<< Chapter < Page Chapter >> Page >

The acceleration due to gravity near the earth surface is nearly constant and equal to 9.8 m / s 2 . Value of ‘g’ is taken as 10 m / s 2 as an approximation to facilitate ease of calculation.

When only acceleration due to gravity is considered, neglecting other forces, each of the bodies (feather and iron ball) starting from rest is accelerated at the same rate. Velocity of each bodies increases by 9.8 m/s at the end of every second. As such, the feather and the iron ball reach the surface at the same time and at the same velocity.

Additional equations of motion

A close scrutiny of three equations of motion derived so far reveals that they relate specific quantities, which define the motion. There is possibility that we may encounter problems where inputs are not provided in the manner required by equation of motion.

For example, a problem involvoing calaculation of displacement may identify initial velocity, final velocity and acceleration as input. Now, the equation of motion for displacement is expressed in terms of initial velocity, time and acceleration. Evidently, there is a mis-match between what is given and what is required. We can, no doubt, find out time from the set of given inputs, using equation for velocity and then we can solve equation for the displacement. But what if we develop a relation-ship which relates the quantities as given in the input set! This would certainly help.

From first equation :

v = u + a t v - u = a t t = ( v - u ) a = a t

From second equation :

( u + v ) 2 = ( x 2 - x 1 ) t ( u + v ) = 2 ( x 2 - x 1 ) t

Eliminating ‘t’,

( u + v ) = 2 a ( x 2 - x 1 ) ( v - u ) v 2 - u 2 = 2 a ( x 2 - x 1 )

v 2 - u 2 = 2 a ( x 2 - x 1 )

This equation relates initial velocity, final velocity, acceleration and displacement.

Also, we observe that equation for displacement calculates displacement when initial velocity, acceleration and time are given. If final velocity - instead of initial velocity - is given, then displacement can be obtained with slight modification.

Δ x = x 2 - x 1 = u t = 1 2 a t 2

Using v = u + at,

Δ x = x 2 - x 1 = ( v - a t ) t + 1 2 a t 2

Δ x = x 2 - x 1 = v t - 1 2 a t 2

Constant acceleration in one dimensional motion

Problem : A train traveling on a straight track moves with a speed of 20 m/s. Brake is applied uniformly such that its speed is reduced to 10 m/s, while covering a distance of 200 m. With the same rate of deceleration, how far will the train go before coming to rest.

Solution : To know the distance before train stops, we need to know the deceleration. We can find out deceleration from the first set of data. Here, u = 20 m/s ; v = 10 m/s ; x = 200 m ; a = ? An inspection of above data reveals that none of the first three equations of motion fits the requirement in hand, while the additional form of equation v 2 - u 2 = 2 a x serves the purpose :

a = v 2 - u 2 2 x = 10 2 - 20 2 2 x 200 = - 3 4 m / s 2

For the train to stops, we have

u = 20 m / s ; v = 0 m / s ; a = - 3 4 m / s 2 ; x = ?

and,

x = v 2 - u 2 2 a = 0 2 - 20 2 2 x ( - 3 4 ) = 266.67 m

Got questions? Get instant answers now!

Displacement in a particular second

The displacement in a second is obtained by subtracting two displacements in successive seconds. We calculate displacements in n th second and (n-1) th seconds. The difference of two displacements is the displacement in the n th second. Now, the displacements at the end of n and (n-1) seconds as measured from origin are given by :

Questions & Answers

A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply

Get the best Physics for k-12 course in your pocket!





Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask