A particle is moving along a curve. Select the correct statement.
1. | If its speed is constant, then it has no acceleration. |
2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |
3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |
4. | If its speed is constant, its acceleration is perpendicular to its velocity. |
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:
1. | 2. | ||
3. | 4. |
A particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:
1. | Acceleration is zero at \(t=1\) sec. |
2. | Speed is zero at \(t=0\) sec. |
3. | Acceleration is always zero. |
4. | Speed is \(3\) m/s at \(t=1\) sec. |
Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |
3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |
Which of the following statements is incorrect?
1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
If a body is accelerating, then:
1. | it must speed up. |
2. | it may move at the same speed. |
3. | it may move with the same velocity. |
4. | it must slow down. |
A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\))
1. | \(20\) m | 2. | \(10\) m |
3. | \(40\) m | 4. | \(400\) m |
An object of mass m is projected from the ground with a momentum \(p\) at such an angle that its maximum height is \(\frac{1}{4}\)th of its horizontal range. Its minimum kinetic energy in its path will be:
1. | \(\frac{p^2}{8 m} \) | 2. | \(\frac{p^2}{4 m} \) |
3. | \(\frac{3 p^2}{4 m} \) | 4. | \(\frac{p^2}{m}\) |
A particle moving on a curved path possesses a velocity of \(3\) m/s towards the north at an instant. After \(10\) s, it is moving with speed \(4\) m/s towards the west. The average acceleration of the particle is:
1. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) south to east. |
2. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) west to north. |
3. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) east to north. |
4. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) south to west. |