The equation of motion and its derivation - class-XI
the equation of motion and its derivation
Questions
Derivation of second equation of motion is:
- $d\theta= w d2t$
- $d\theta= w dt$
- $d\theta= w d3t$
- $d\theta= w dt^{2}$
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 :
- newton's Ist law
- newton's IInd law
- newton's IIIrd law
- none of the above
For a body moving with an initial velocity $u$ and uniform acceleration $a$. Find the displacement of the body in time t.
- $s=ut+\dfrac{1}{2}at^2$
- $s=u+at$
- $s=ut-\dfrac{1}{2}at^2$
- $s=ut+at^2$
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?
- $S \propto t^2$
- $S \propto t$
- $S \propto \dfrac{1}{t^2}$
- $S \propto \dfrac{1}{t}$
The correct equation of motion is :
- $v=u+aS$
- $v=ut+a$
- $S= ut +\frac{1}{2} at$
- $v = u + at$
In the equation of motion, $S = ut + 1/2 at^2$, S stands for
- displacement in t seconds
- maximum height reached
- displacement in the $t^{th}$ second
- none of these
Gradient of line of displacement-time graph gives the :
- acceleration
- velocity
- displacement
- none of these
Gradient of line of velocity-time graph gives :
- distance
- time
- velocity
- acceleration
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
- $850m$
- $1000m$
- $1250m$
- $2250m$
At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the platform with $a = - 0.5m/{s^2}$ relative to the platform. The platform moves with a constant speed $v = + 1.0m/s$ relative to the stationary floor. In $4.0$ seconds, how much will the child have been displaced relative to the floor?
- $8m$
- $0m$
- $3m$
- $4m$
An open lift is moving upwards with velocity $10m/s$. It has an upward acceleration of $2m/{s^2}$. A ball is projected upwards with upwards with velocity $20m/s$ relative to the ground. Find the time when the ball again meets the lift.
- $\frac{5}{3}s$
- $\frac{4}{3}s$
- $\frac{3}{4}s$
- $\frac{1}{4}s$
An elevator car whose floor-to-ceiling distance is equal to 2.7m starts ascending with a constant acceleration $1.2m/{s^2};2.0s$ after the start a bolt begins falling from the ceiling of the car. Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.
- 0.7 m
- 1.7 m
- 2.7 m
- 3.7 m
A boy sitting on the top most berth in the compartment of a train which is just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about 2 m. The apple will fall
- In the hand of his brother
- Slightly away from the hand of his brother in the direction of the motion of the train.
- Slightly away from the hands of his brother in the direction opposite to the direction of the motion of the train.
- None of these
The distance covered by a body moving alone-X-axis with initial velocity 'u' and uniform acceleration 'a' is given by $\displaystyle x=ut+\frac{1}{2}at^{2}$. This result is a consequence of
- Newton's Ist law
- Newton's IInd law
- Newton IIIrd law
- None of the above
A cart begins from rest at the top of a long incline and rolls with a constant acceleration of $2m/s^{2}$. How far has the cart moved along the incline after rolling for $3$ seconds?
- $3$ meters
- $6$ meters
- $9$ meters
- $18$ meters
A car was travelling at a speed of 10 m/s. After the brakes were applied, it start to decelerate at a rate of 2 $m/s^2$ and finally came to rest. Find the distance traveled by the car before coming to rest.
- 10 m
- 15 m
- 25 m
- 35 m
The initial velocity of a particle (at $t = 0$) is $u$ and the acceleration by $f$ of particle at time $t$ is given $f=at$. Where $a$ is a constant which of the following relation for velocity $v$ of particle after time $t$ is turn
- $v\, =\, u\, +\, at^2$
- $v\, =\, u\, +\, \displaystyle \frac{at^2}{2}$
- $v\, =\, u\, +\, at$
- $v\, =\, u$