Tag: physics

Questions Related to physics

Derivation of second equation of motion is:

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $d\theta= w d2t$

  2. $d\theta= w dt$

  3. $d\theta= w d3t$

  4. $d\theta= w dt^{2}$

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Correct Option: B
Explanation:

$S= ut+\frac{1}{2} at^2$
$\theta = w _0t +\frac{1}{2}\alpha t^2$
$w= \frac{d\theta}{dt}$
$d\theta= w dt$

The distance $x$ covered in time $t$ by a body having initial velocity ${ v } _{ 0 }$ and having constant acceleration $a$ is given by $x={ v } _{ 0 }t+1/2a{ t }^{ 2 }$. This result follows from :

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. newton's Ist law

  2. newton's IInd law

  3. newton's IIIrd law

  4. none of the above

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Correct Option: D
Explanation:

The given equation is the fundamental equation of kinematics. So it can not follow from any Newton's law of motion.
Ans:(D)

A ladder of length 10 m and mass 20 kg (and with uniform mass distribution) leans against a slippery vertical wall. The ladder makes an angle of $30^{\circ}$ with respect to the vertical. Friction between the ladder and the ground prevents it from sliding downwards. What is the magnitude of the force exerted on the ladder by the wall?
$[Take \sqrt { 3 } =1.732;g=10{ m/s }^{ 2 }]$

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $0 N$

  2. $0.58 N$

  3. $58 N$

  4. $5.8 N$

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Correct Option: C

For a body moving with an initial velocity $u$ and uniform acceleration $a$. Find the displacement of the body in time t.

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $s=ut+\dfrac{1}{2}at^2$

  2. $s=u+at$

  3. $s=ut-\dfrac{1}{2}at^2$

  4. $s=ut+at^2$

Show answer
Correct Option: A
Explanation:

From the second equation of motion, if u = initial velocity , a= acceleration and t= time then

$s=ut+\dfrac{1}{2}at^2$

How is the distance related with time for the motion under uniform acceleration such as the motion of a freely falling body starting from rest?

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $S \propto t^2$

  2. $S \propto t$

  3. $S \propto \dfrac{1}{t^2}$

  4. $S \propto \dfrac{1}{t}$

Show answer
Correct Option: A
Explanation:

For a free falling body, initial velocity, $u = 0 m/s $ and acceleration due to gravity, $a = g$.
Putting the values of $u$ and $a$ in the equation of motion, $S = ut+\dfrac{1}{2}at^2 $
We get, $S = \dfrac{1}{2}gt^2$
Therefore, $S \propto t^2$

The correct equation of motion is :

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $v=u+aS$

  2. $v=ut+a$

  3. $S= ut +\frac{1}{2} at$

  4. $v = u + at$

Show answer
Correct Option: D
Explanation:

Three equations of motion are as follows:

$v=u+at$

$S = ut+\dfrac{1}{2}at^2$

$v^2 = u^2+2aS$

In the equation of motion, $S = ut + 1/2 at^2$, S stands for

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. displacement in t seconds

  2. maximum height reached

  3. displacement in the $t^{th}$ second

  4. none of these

Show answer
Correct Option: A
Explanation:

$ S=ut+\dfrac { 1 }{ 2 } a{ t }^{ 2 }$

where 
S= Distance traveled in the t seconds
u= Initial velocity of the motion 
a= acceleration or retardation of the motion 

Gradient of line of displacement-time graph gives the :

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. acceleration

  2. velocity

  3. displacement

  4. none of these

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Correct Option: B
Explanation:
Slope of line of displacement time graph$=\cfrac { ds }{ dt } $
The rate of change of position i.e., rate of change of displacement with time is called velocity

Gradient of line of velocity-time graph gives :

physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. distance

  2. time

  3. velocity

  4. acceleration

Show answer
Correct Option: D
Explanation:
Gradient of line is basically a slope of line
Slope$=\cfrac { \triangle y }{ \triangle x } $
Here, Slope $=\cfrac { d\upsilon  }{ dt } $
As we all know acceleration is the rate of change of velocity with time
$\therefore $ acceleration $=\cfrac { d\upsilon  }{ dt } $

Two trains A and B each of length 400m Are moving on two parallel tracks The same direction (while A is ahead of B) With same speed 72 km / h.The driver of B decides to overtake And accelerate by $1m/{ s }^{ 2 }$. If after 50 seconds B Just brushes past A, Calculate the original distance between A and B


physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

  1. $850m$

  2. $1000m$

  3. $1250m$

  4. $2250m$

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Correct Option: A