Integration

Q. At the moment $t=0$ particle leaves origin and moves in the positive direction of $x$-axis. Its velocity as a function of time is given as $v=(5-t)\text{m/s}$. $x$-coordinate of particle at $t=2\text{s}$ is

1. 8 m
2. 6 m
3. 10 m
4. 12 m

Q. A particle moving in a straight line such that $v=3t^2+4t+1$. Its average velocity during time interval $t=0\text{to}t=t$ is

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

Q. The mathematical tool that we use to find the change in velocity from a function of acceleration with respect to time is called integration.

1. True
2. False

Q. A particle moves along a straight line and its velocity depends on time as $v=4t-t^2.$ Then for first $5\text{s}$

1. Average velocity is $\frac{25}{3}\text{m}$
2. Average speed is $10{\text{ms}}^{-1}$
3. Average velocity is $\frac{5}{3}{\text{ms}}^{-1}$
4. Acceleration is $4{\text{ms}}^{-2}\text{at}t=0$

Q. An object is at $2\text{m}$ at $t=0\text{sec}$. Its velocity is given by $v=2t+7$, its position at $t=5\text{sec}$ is

1. $52\text{m}$
2. $62\text{m}$
3. $65\text{m}$
4. $55\text{m}$

Q. A particle is moving rectilinearly so that its acceleration is given as $a\left(m/s^2\right)=3t^2+1$ Its initial velocity is zero then the velocity of the particle at $t=1$ s will be

1. $2\text{m/s}$
2. $5\text{m/s}$
3. $3\text{m/s}$
4. $4\text{m/s}$

Q. The flux passing through the surface $S_5$ will be

1. $-0.135N{m}^2{C}^{-1}$
2. $-0.054N{m}^2{C}^{-1}$
3. $-0.081N{m}^2{C}^{-1}$
4. $-0.054N{m}^2{C}^{-1}$

Q. A particle is moving with speed $v=b\sqrt{x}$ along the positive $x$ - axis. Calculate the speed of the particle at time $t=\tau$. (Assume that the particle is at the origin at $t=0$).

1. $\frac{b^2\tau }{4}$
2. $\frac{b^2\tau }{2}$
3. $b^2\tau$
4. $\frac{b^2\tau }{\sqrt{2}}$

Q. The mathematical tool that we use to find the change in velocity from a function of acceleration w.r.t time is