Instantaneous Velocity

Q.

The acceleration of a moving body can be found from

1. Slope of the velocity-time graph

2. Slope of distance-time graph

3. Area under velocity-time graph

4. Area under distance-time graph

Q.

An electron starting from rest has a velocity that increases linearly with time as $v=kt$, where $k=2m{s}^{-2}$. The distance travelled in the first 3 seconds will be

1. 27 m

2. 36 m

3. 9 m

4. 16 m

Q. The velocity of a particle at time t is given by the relation $v=6t-\frac{t^2}{6}$. The distance traveled in 3 seconds is, if s=0 at t=0

1. $\frac{57}{2}$
2. $\frac{39}{2}$
3. $\frac{51}{2}$
4. $\frac{33}{2}$

Q. Statement-1: If displacement is a linear function of time, its average and instantaneous velocity will be same.
Statement-2: If the acceleration of a moving particle is zero, the particle continues to move along the same direction.

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 and 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. A displacement $s$ v/s time $t$ curve of a particle is shown in the figure. The maximum instantaneous velocity $v_m$ of the particle is around the point

1. $S$ with $v_m\approx 2m/s$
2. $R$ and $v_m\approx 2m/s$
3. $Q$ and $v_m\approx 1m/s$
4. $R$ and $v_m\approx 0.5m/s$

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

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

Q. A car starts with $10\frac{m}{s}$ and accelerates with constant acceleration of $5\frac{m}{s^2}$. Find the final speed achieved by the car after $10$ sec.

1. $60\frac{m}{s}$
2. $50\frac{m}{s}$
3. $40\frac{m}{s}$
4. $25\frac{m}{s}$

Q. A particle's motion is given by $s=a(t+b(e^{(-\frac{t}{b})}-1))$, where ($s$ is in metre, $a$ and $b$ are constants and $t$ is in sec). What will be the instantaneous speed of the particle at $t=\infty$

1. $\infty$
2. $a$
3. $b$
4. $0$

Q. The displacement of a particle varies with time $t$ as: $s=\alpha t-\beta t^2$. Determine the time $\left(t\right)$ at which velocity of the particle becomes $0$.

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