Tag: the equation of motion and its derivation

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

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 :

  1. newton's Ist law

  2. newton's IInd law

  3. newton's IIIrd law

  4. none of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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?
$[Take \sqrt { 3 } =1.732;g=10{ m/s }^{ 2 }]$

  1. $0 N$

  2. $0.58 N$

  3. $58 N$

  4. $5.8 N$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using torque equilibrium about the base: (Weight * L/2 * sin(30)) = (Force_wall * L * cos(30)). Thus Force_wall = (Weight/2) * tan(30). Weight = 20kg * 10m/s^2 = 200N. Force_wall = 100 * (1/sqrt(3)) = 100 / 1.732 = 57.73 N, which rounds to 58 N.

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

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

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

  2. $s=u+at$

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

  4. $s=ut+at^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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?

  1. $S \propto t^2$

  2. $S \propto t$

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

  4. $S \propto \dfrac{1}{t}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $S \propto t^2$

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

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

  1. displacement in t seconds

  2. maximum height reached

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

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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 

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

Gradient of line of velocity-time graph gives :

  1. distance

  2. time

  3. velocity

  4. acceleration
Reveal answer Fill a bubble to check yourself
D Correct answer
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 } $
Multiple choice physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

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


  1. $850m$

  2. $1000m$

  3. $1250m$

  4. $2250m$
Reveal answer Fill a bubble to check yourself
A Correct answer