Instantaneous velocity

Q. The velocity of a particle moving with constant acceleration at time $t_0$ is $10\text{m/s}$. After $5\text{second}$, velocity is $20\text{m/s}$. The velocity $3\text{sec}$ before time $t_0$ is

1. $8\text{m/s}$
2. $4\text{m/s}$
3. $6\text{m/s}$
4. $7\text{m/s}$

Q. A particle is accelerating at $a=2x$ and initially it was at $x=2\text{m}$ moving with $3\text{m/s}$. Then find out the velocity at position $x=5\text{m}$.

1. $7\text{m/s}$
2. $\sqrt{31}\text{m/s}$
3. $\sqrt{28}\text{m/s}$
4. $\sqrt{51}\text{m/s}$

Q. A force of $2\text{N}$ acts on a body of $20\text{kg}$. As, a result, the body covers $100\text{cm}$ in $4\text{s}$, moving along a straight line. Find the initial velocity.

1. $0\text{cm/s}$
2. $7\text{cm/s}$
3. $5\text{cm/s}$
4. $8\text{cm/s}$

Q. Slope of the of a position- time graph gives us instantaneous velocity.

1. Secant
2. Tangent
3. Chord

Q. A force of $2\text{N}$ acts on a body of $20\text{kg}$. As, a result, the body covers $100\text{cm}$ in $4\text{s}$, moving along a straight line. Find the initial velocity.

1. $0\text{cm/s}$
2. $7\text{cm/s}$
3. $5\text{cm/s}$
4. $8\text{cm/s}$

Q. A man of height $h$ walks in a straight path towards a lamp post of height $H$ with velocity $v$. Then velocity of the edge of the shadow on the ground will be

1. $\frac{hv}{(H-h)}$
2. $\frac{Hv}{(H-h)}$
3. $\frac{hv}{(H+h)}$
4. $\frac{(H-h)}{hv}$

Q. A body initially at rest is moving along x-axis in such a way that its acceleration vs displacement plot is as shown in figure. What will be the maximum velocity of particle in m/sec?

1. 1
2. 2
3. 3
4. 5

Q. A force of $2\text{N}$ acts on a body of $20\text{kg}$. As, a result, the body covers $100\text{cm}$ in $4\text{s}$, moving along a straight line. Find the initial velocity.

1. $0\text{cm/s}$
2. $7\text{cm/s}$
3. $5\text{cm/s}$
4. $8\text{cm/s}$

Q. Statement -1 : Let $v$ be the speed of particle at any time $t$. If $\frac{dv}{dt}$ is a non - zero constant then speed of particle may be minimum at some time.
Statement -2 : The speed $v$ of a moving particle may be minimum at time $t=t_0$ when $v=0$. The speed $v$ of a moving particle may also be minimum at time $t=t_0$ when $\frac{dv}{dt}=0$ and $\frac{d^{2}v}{d{t}^2}=$ positive.

1. Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.
2. Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1.
3. Statement 1 is correct and statement 2 is incorrect.
4. Statement 1 is incorrect and statement 2 is correct.

Q. The position of the particle is given by $x=(3t^2-e^t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

1. $2t-e^t$
2. $3t+e^t$
3. $6t-e^t$
4. $6t^2-e^t$

Q. A particle moves in a straight line with an acceleration 'a' $m/s^2$ given as function of time, $a=\frac{-1}{t^2}$. At time t = 1 s the particle has velocity of 3 m/s, then find the velocity at t = 4 s.

1. 2.25 m/s
2. 5 m/s
3. 4.5 m/s
4. 7 m/s

Q. How small is an instant?

1. Very small time interval
2. Zero time interval
3. Infinitesimally small time interval
4. Not defined

Q. A bullet inside a sniper's barrel when fired has a speed which can be expressed $v=(-{10}^7{t}^2+{10}^{5}t)m/s$, where $t$ is in seconds. Additionally, it was observed that the acceleration of the bullet is zero when it reaches the tip of the barrel. (Consider bullet to be a point object)

1. The bullet reaches the tip of the barrel at $t=0.01s$.
2. Speed at which the bullet leaves the barrel is $250m/s$.
3. Length of the barrel is below $1m$.
4. At $t=0.5s$, the magnitude of the acceleration of the bullet is $9.9\times {10}^{5}m/s^2$

Q. Which of these statement(s) is/are correct?

1. Instantaneous Velocity = Rate of change of position with time
2. Instantaneous Velocity = $\frac{\text{Infinitesimal Displacement}}{\text{Infinitesimal Time Interval}}$
3. Instantaneous Velocity = Slope of tangent at a point on $x-t$ graph
4. Instantaneous Velocity = $\frac{\text{Total Displacement}}{\text{Total Time Taken}}$

Q. Which of the following represents the instantaneous velocity?

1. ${lim}_{\Delta t\to 0}\frac{\Delta \overrightarrow{S}}{\Delta t}$
   
2. $\frac{\Delta \overrightarrow{S}}{\Delta t}$
3. $\frac{S}{\Delta t}$
4. None of the above

Q. Acceleration of the particle in a rectilinear motion is given as $a=3t^2-2t+5$ in $\left(m/s^2\right)$. The velocity of the particle as a function of time $t$ is
(Given, at $t=0,u=-4m/s$)

1. $t^3-t^2+5t+4$
2. $t^3-t^2+5t$
3. $t^3-t^2+5t-4$
4. $t^3+t^2+5t$

Q. A particle moves in a straight line with an acceleration 'a' $m/s^2$ given as function of time, $a=\frac{-1}{t^2}$. At time t = 1 s the particle has velocity of 3 m/s, then find the velocity at t = 4 s.

1. 2.25 m/s
2. 5 m/s
3. 4.5 m/s
4. 7 m/s

Q. The position of the particle is given by $x=(e^t-\cos t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

1. $e^t-\sin t$
2. $e^t-\sec t$
3. $e^t+\tan t$
4. $e^t+\sin t$

Q. Acceleration of the particle in a rectilinear motion is given as $a=3t^2-2t+5$ in $\left(m/s^2\right)$. The velocity of the particle as a function of time $t$ is
(Given, at $t=0,u=-4m/s$)

1. $t^3-t^2+5t+4$
2. $t^3-t^2+5t$
3. $t^3-t^2+5t-4$
4. $t^3+t^2+5t$

Q.

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

1. 7

2. 8

3. 9

4. 4

Q. The displacement of a particle is given by $x=4t^2+2t$ in $\text{m}$. Its instantaneous velocity at $2s$ is

1. $16\text{m/s}$
2. $18\text{m/s}$
3. $22\text{m/s}$
4. $36\text{m/s}$

Q. PSLV launches a rocket in a gravity free space with constant acceleration $5{\text{m/s}}^2$ along +x direction (see figure). The length of the chamber inside the rocket is $6\text{m}$. At time $t=0$, a ball is thrown from the left end of the chamber in +x direction with a speed $0.7\text{m/s}$ relative to the rocket. At the same time, another ball is thrown in opposite direction to the previous ball with a speed $0.3\text{m/s}$ relative to the rocket. The time in seconds when the two balls hit each other is

Q. The velocity of a particle moving with constant acceleration at time $t_0$ is $10\text{m/s}$. After $5\text{second}$, velocity is $20\text{m/s}$. The velocity $3\text{sec}$ before time $t_0$ is

1. $8\text{m/s}$
2. $4\text{m/s}$
3. $6\text{m/s}$
4. $7\text{m/s}$

Q. PSLV launches a rocket in a gravity free space with constant acceleration $5{\text{m/s}}^2$ along +x direction (see figure). The length of the chamber inside the rocket is $6\text{m}$. At time $t=0$, a ball is thrown from the left end of the chamber in +x direction with a speed $0.7\text{m/s}$ relative to the rocket. At the same time, another ball is thrown in opposite direction to the previous ball with a speed $0.3\text{m/s}$ relative to the rocket. The time in seconds when the two balls hit each other is

Q. A particle starts from rest. Its acceleration at time $t=0$ is $5{\text{ms}}^{-2}$ which varies with time as shown in figure. The maximum speed of the particle will be

1. $7.5{\text{ms}}^{-1}$
2. $15{\text{ms}}^{-1}$
3. $30{\text{ms}}^{-1}$
4. $7.5{\text{ms}}^{-1}$

Q. A particle starting from rest undergoes acceleration given by $a=|t–2|{\text{m/s}}^2$ where, $t$ is time in second. Velocity of particle after $4\text{sec}$ is

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $8\text{m/s}$
4. $4\text{m/s}$

Q.

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

1. 7

2. 8

3. 9

4. 4

Q.

The position of an elevator varies with time according to this function

$p\left(t\right)=x^2+2x+3$

What will be the velocity of the elevator at time t = 4 secs

___

Q. The motion of a particle along a straight line is described by equation $x=12t-t^3$ where $x$ is in meter and $t$ is in second. The time instant when velocity of the particle becomes zero is

1. $2\text{s}$
2. $1\text{s}$
3. $4\text{s}$
4. $3\text{s}$

Q.

The position of a particle travelling along x - axis is given by $x_t$ = $t^3$ - 9 $t^2$ + 6t where $x_t$ is in m and t is in second . Then

1) the particle does not come to rest at all.

2) the particle comes to rest firstly at (3 - $\sqrt{7}$ ) s and then at (3 + $\sqrt{7}$) s

3) the speed of the particle at t= 2s is 18 m$s^{-1}$

4) the acceleration of the particle at t= 2s is 6 m$s^{-2}$

1. 2, 3, 4 are correct

2. 2, 3 are correct

3. All of them are correct

4. 1 and 2 are correct