Q. No.A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}\). 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 \(\mathrm{v}_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2 \mathrm{v}_0 \sin \frac{\theta}{2} \) | 1. | \( \mathrm{v}_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 \mathrm{v}_0 \cos \frac{\theta}{2} \) | 4. | \( \mathrm{v}_0 \cos \frac{\theta}{2}\) |
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 \(|\frac{d\vec{v}}{dt}|\neq0\) but \(\frac{d|\vec{v}|}{dt}=0\) |
| 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 \(|\frac{d\vec{v}}{dt}|=0\) but \(\frac{d|\vec{v}|}{dt}\neq0\) |
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 m/)
| 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 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 , 37° south to east |
| 2. | 0.25 , 37° west to north |
| 3. | 0.5 , 37° east to north |
| 4. | 0.5 , 37° south to west |
A bus is going to the North at a speed of 30 kmph. It makes a 90° left turn without changing the speed. The change in the velocity of the bus is:
| 1. | 30 kmph towards W |
| 2. | 30 kmph towards S-W |
| 3. | 42.4 kmph towards S-W |
| 4. | 42.4 kmph towards N-W |
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