Instantaneous velocity

Q.

What is the full form of MIPs in the computer?

Q. The instantaneous velocity of a particle moving in a straight line is given as $v=\alpha t+\beta t^2$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between $1\text{s}$ and $2\text{s}$ is

1. $3\alpha +7\beta$
2. $\frac{3}{2}\alpha +\frac{7}{3}\beta$
3. $\frac{\alpha }{2}+\frac{\beta }{3}$
4. $\frac{3}{2}\alpha +\frac{7}{2}\beta$

Q.

The speed $v$ of a particle moving along a straight line is given by $a+b{v}^2=x^2$ (where $x$ is its distance from the origin). The acceleration of the particle is

1. $bx$

2. $\frac{x}{a}$

3. $\frac{x}{b}$

4. $\frac{x}{ab}$

Q.

A body is moving with uniform acceleration and describes 75 m in the 6th second and 115 m in the 11th second. Show that its moves 155 m during the 16th second.

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 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. 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. 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 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

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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

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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. 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. A car moves along a straight line whose equation of motion is given by $s=24t+3t^4–2t^3$, where $s$ is in metre and $t$ is in second. The velocity of the car at $t=0$ will be

1. $7\text{m/s}$
2. $9\text{m/s}$
3. $12\text{m/s}$
4. $24\text{m/s}$

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 instantaneous velocity of a particle moving in a straight line is given as $v=\alpha t+\beta t^2$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between $1\text{s}$ and $2\text{s}$ is

1. $3\alpha +7\beta$
2. $\frac{3}{2}\alpha +\frac{7}{3}\beta$
3. $\frac{\alpha }{2}+\frac{\beta }{3}$
4. $\frac{3}{2}\alpha +\frac{7}{2}\beta$

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 car moves along a straight line whose equation of motion is given by $s=24t+3t^4–2t^3$, where $s$ is in metre and $t$ is in second. The velocity of the car at $t=0$ will be

1. $7\text{m/s}$
2. $9\text{m/s}$
3. $12\text{m/s}$
4. $24\text{m/s}$

Q. The motion of a particle along a straight line is described by the function $x=(2t-3{)}^2$ where $x$ is in meters and $t$ is in seconds. Find the velocity of the particle at the origin.

1. $0\text{m/s}$
2. $1\text{m/s}$
3. $2\text{m/s}$
4. $3\text{m/s}$

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. 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 particle moves along the $x-$axis in such a way that its $x-$ coordinates varies with time as $x=1–2t+3t^2$. What will be its initial velocity?

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

Q. A particle moves along the $x-$axis in such a way that its $x-$ coordinates varies with time as $x=1–2t+3t^2$. What will be its initial velocity?

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

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 particle starts its motion from point A in the positive x direction in such a way that after every t sec it is at a distance of $t^2$ from the starting point. Find its instantaneous velocity at $t=4^{th}$ sec also the rate at which velocity changes.

1. v = 8 m/s rate of velocity change = 2

2. v = 16 m/s rate of velocity change = 4

3. v = 8 m/s rate of velocity change = 8

4. v = 16 m/s rate of velocity change = 16

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

1. Secant
2. Tangent
3. Chord