## Motion in one dimension Problem

# The relation between time t and distance x is t = αx^{2 }+ βx, where α & β are constants, then the retardation is

Sriyathmika asked

**Asnwer**

Given t = αx^{2} + βx

dt/dt = 2αx.dx/dt + β.dx/dt

1 = 2αxv + βv

v.(2αx + β) = 1

(2αx + β) = 1/v

Again differentiate both side with respect to time (t)

2α.dx/dt = -v

^{-2}. dv/dt

2αv = v

^{-2}. acceleration

acceleration = -2αv

^{3}

^{3}

## CRUISE LIFT VEHICLE

A vehicle cruises at a speed of 3 km/s at an altitude of 25 km. It has a mass of 100,000 kg, and it has a lifting surface area of 300 . Take the radius of the Earth to be 6400 km, and the value of ‘g’ to be 9.8 ms-1 . The lift to drag ratio is 5.

Both answers should be given in N.

How much lift must it generate?

How much thrust must the propulsion system generate?

(**JH**)

## Hypersonic Equivalence Principle

A piston moves along a tube containing air at an initial sound speed of 330 m/s. When the piston velocity is 250 m/s, it drives a shock wave which propagates at a velocity of 500 m/s. When the piston velocity is 100 m/s, it drives a shock at 392 m/s.

Use the hypersonic equivalence principle to calculate the shock angles (in degrees) on a flat plate:

At an incidence of 6 degrees and a Mach number of 7.2

At an incidence of 2 degrees and a Mach number of 21.7

Then calculate:

The incidence degrees required to produce a shock angle of 9.5 degrees at a Mach number of 7.2

The incidence () required to produce a shock angle () of 3.2 degrees at a Mach number of 21.7

(**JH**)

## A QUESTION ABOUT SPACE-TIME

Here is a system which is travelling left to right at the speed of 0.5c (half of the speed of light). The system is made of two parts. Both the parts are made of a light source and a light receiver or detector; but both are placed opposite to each other (that means the receivers are at the ends of the system).

Then the both sources emit light at the same time and the receivers receive the pulse. According to Maxwell’s equations, the speed of the pulse of light will not be affected by the speed of its source (and the system). We know that the speed of light is same for all observers. So, the receivers will receive the light at the same time. But here rises a problem: how relativity will explain this phenomenon (that the speed of light is constant here too). Here, we should remember that the system is travelling at 0.5c and we can’t use the length contraction and time delay. Why? It is because:

1. If the system is affected with length contraction and time delay, both the parts will be affected not a single part. So, if we try to explain how the speed of light become constant in the right part with length contraction and time delay, we shall be unable to explain how the speed of light become constant in the left part with the same length contraction and time delay!

2. If we suppose that the receivers received those pulses at different time, it will become clear that the speed of light is not same and constant for all observers and the theory of relativity will break down!

Am I right? Please reply.

From

Ritu Lahkar

## Adieu !! Stephen Hawking …..

Stephen Hawking, the world renowned Physicist, the inspiration to millions, who outlived doctors’ predictions after suffering from progressive motor neuron disease and rised to the most coveted chair in Physics…The author of “A Brief History of Time” and many such inspiring books …. finally passed away at the age of 76.

AskPhysics family expresses its deepest condolences

You could barely move your limbs and body, but you moved our hearts and minds and compelled us to think deep and wide pondering the mysteries in connection with the evolution of universe and the future.

Adieu !! Hawking… Your discoveries, theories and books will continue to inspire us!

## Randomness and The Universe

Is anything truly random? Is random a human made idea to describe something that is hard to predict? Or is it possible for something to actually be random?

If nothing is truly random then if the universe was created again, would everything turn out the same? I don’t see why it wouldn’t but im not finding much about this online and i want to know what you think.

Thank You

Jack

## Bravais Lattices/Particle Physiscs

I have a few exercices (two) on Bravais lattices and I can’t figure it out about the best way to approach them. A few tips on the steps, or theories that I should base my resolution on would be helpful.

I also have another 2 exercices that approach particles collision times and the kinetic theory of gases.

By the way, the exercises I mention are attached.

If there is any helpull suggestion that allows me to solve this problems, I would be very happy.

Thanks.

Patrícia