Velocity

Q. The position of a particle moving along x-axis is given by $x=(t^2-15t+10)\text{m}$, where $t$ is in second. Find the time when particle comes at rest?

1. $8.5\text{s}$
2. $7.5\text{s}$
3. $6.5\text{s}$
4. $10.5\text{s}$

Q. A ball of mass $m$ is suspended by a thread of length $l$. With what minimum velocity has the point of suspension to be shifted in the horizontal direction for the ball to move along the circle about the point?

1. $\sqrt{3gl}$
2. $\sqrt{5gl}$
3. $\sqrt{7gl}$
4. $\sqrt{2gl}$

Q. Two blocks are connected by a string, as shown in figure. They are released from rest. The coefficient of kinetic friction between the upper block and the surface is 0.5. Assume that the pulley is massless and frictionless. Their common speed after they have moved a distance $5m$ will be: ($g=10m{s}^{-2}$)

1. $10\text{m/s}$
2. $5\text{m/s}$
3. $2.5\text{m/s}$
4. $25\text{m/s}$

Q. A particle is projected making an angle of ${45}^{\circ }$ with horizontal, with kinetic energy $K$. The kinetic energy at highest point will be

1. $\frac{K}{\sqrt{2}}$
2. $\frac{K}{2}$
3. $2K$
4. $K$

Q. The motion of a particle along a straight line is described by the function $x=6+4t^2–t^4$ where $x$ is in meters and $t$ is in seconds. What is the maximum velocity attained by the particle ?

1. $\frac{16}{3}\sqrt{\frac{2}{3}}\text{m/s}$
2. $\frac{14}{3}\sqrt{\frac{2}{3}}\text{m/s}$
3. $\frac{14}{3}\sqrt{\frac{3}{2}}\text{m/s}$
4. $\frac{16}{3}\sqrt{\frac{3}{2}}\text{m/s}$

Q. The position of a particle moving along x-axis is given by $x=(t^2-15t+10)\text{m}$, where $t$ is in second. Find the time when particle comes at rest?

1. $8.5\text{s}$
2. $7.5\text{s}$
3. $6.5\text{s}$
4. $10.5\text{s}$

Q. The velocity of the tip of the second hand of a watch is $10\text{cm/s}$. The change in velocity of its tip in $15\text{s}$ is

1. zero
2. $\frac{20}{\sqrt{2}}\text{cm/s}$
3. $\frac{10}{\sqrt{2}}\text{cm/s}$
4. $10\text{cm/s}$

Q. A train of length $100\text{m}$ is crossing a bridge $200\text{m}$ long in length at the speed of $72\text{kmph}$. What is the time taken by the train to cross the bridge?

1. 5 seconds
2. 10 seconds
3. 15 seconds
4. 20 seconds

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. The position of the particle is given by $x=2t^2+6t+2$ in $\text{m}$. The instantaneous speed of the particle at $6\text{sec}$ is

1. $20\text{m/s}$
2. $30\text{m/s}$
3. $24\text{m/s}$
4. $36\text{m/s}$

Q. The position of the particle is given by $x=2t^2+6t+2$ in $\text{m}$. The instantaneous speed of the particle at $6\text{sec}$ is

1. $20\text{m/s}$
2. $30\text{m/s}$
3. $24\text{m/s}$
4. $36\text{m/s}$

Q. A train of length $100\text{m}$ is crossing a bridge $200\text{m}$ long in length at the speed of $72\text{kmph}$. What is the time taken by the train to cross the bridge?

1. 5 seconds
2. 10 seconds
3. 15 seconds
4. 20 seconds