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Derive the following equations of motion

xz_007 [3.2K]

Answer:

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<h3>a. Let us assume a body has initial velocity 'u' and it is subjected to a uniform acceleration 'a' so that the final velocity 'v' after a time interval 't'. Now, By the definition of acceleration, we have:</h3>

$a = \frac{v - u}{t} \\ or \: at = v - u \\ v = u + at \:$

It is first equation of motion.

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<h3>b. Let us assume a body moving with an initial velocity 'u'. Let it's final body 'v' after a time interval 't' and the distance travelled by the body becomes 's' then we already have,</h3>

$v = u + at...........(i) \\ s = \frac{u + v}{2} \times t.........(ii)$

Putting the value of v from the equation (i) in equation (ii), we have,

$s= \frac{u + (u + at)}{2} \times t \: \: \\ or \: s = \frac{(2u + at)t}{2} \\ or \: s = \frac{2ut + a {t}^{2} }{2} \\ s = ut + \frac{1}{2} a {t}^{2}$

It is third equation of motion.

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<h3>c. Let us assume a body moving with an initial velocity 'u'. Let it's final velocity be 'v' after a time and the distance travelled by the body be 's'. We already have,</h3>

$v = u + at.....(i) \\ s = \frac{u + v}{2} \times t......(ii) \\$

$v = u + at \\ or \: at = v - u \\ t = \frac{v - u}{a}$

Putting the value of t from (i) in the equation (ii)

$s = \frac{u + v}{2} \times \frac{v - u}{a} \\ or \: s = \frac{ {v}^{2} - {u}^{2} }{2a} \\ or \: 2as = {v}^{2} - {u}^{2} \\ {v}^{2} = {u}^{2} + 2as$

It is forth equation of motion.

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Hope this helps...

Good luck on your assignment..

3 0

3 years ago

Technician A says that the rotary engine is not an internal combustion engine, because it does not use pistons. Technician B say

Rama09 [41]

Answer:

Technician B

Step-by-step explanation:

Rotary engine, also known as Wankel, is an internal combustion engine as the definition of inernal combustion is <em>any machine that uses energy from chemical links and transforms it in mechanical work through combustion inside it.</em>

The rotary engine gets three power pulses for each rotation because it can compress, intake/exhaust, and expand at the time in diferent parts of the engine, separated by the tree edges of the triangular rotor.

4 0

3 years ago

A zone reconnaissance involves a directed effort to obtain detailed information on all routes, obstacles, terrain, enemy forces,

son4ous [18]

Answer:

It is True

Explanation:.

A commander assigns a zone reconnaissance mission when he seeks additional information on a zone before committing other forces in the zone. It is appropriate when the enemy situation is vague, existing knowledge of the terrain is limited, or combat operations have altered the terrain. A zone reconnaissance could include several route or area reconnaissance missions assigned to subordinate units.

7 0

3 years ago

Write your own examples of big and small forces on big and small things for

Nady [450]

Answer:

you know what I think you should not give these kind of q

7 0

3 years ago

What is the equivalent capacitance of the three capacitors in the figure?

pantera1 [17]

Where's the figure?.........

8 0

3 years ago