Q. No.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 \(x = \left(t^2 -2t\right)~\text m,\) and \(y = \left(2t^2-t\right)~\text m,\) then:
| 1. | the acceleration is zero at \(t=1~\text s.\) |
| 2. | the speed is zero at \(t=0~\text s.\) |
| 3. | the acceleration is always zero. |
| 4. | the speed is \(3~\text{m/s}\) at \(t=1~\text s.\) |
Rain is pouring vertically downward at a velocity of \(4~\text{km/h}\). The magnitude of the velocity of rain with respect to a man running along the north on a horizontal road at \(3~\text{km/h}\) is:
1. \(7~\text{km/h}\)
2. \(5~\text{km/h}\)
3. \(1~\text{km/h}\)
4. \(3~\text{km/h}\)
A particle is moving with an acceleration of . If at t = 0, its velocity is (i+j) m/s, then its velocity (in m/s) at time t = 2 s is
(1)
(2)
(3)
(4)
It is raining at \(20\) m/s in still air. Now a wind starts blowing with speed \(10\) m/s in the north direction. If a cyclist starts moving at \(10\) m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:
1. \(20\) m/s
2. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s
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 missile is fired for maximum range with an initial velocity of \(20\) m/s, then the maximum height of missile is: (Take \(g=10\) m/s2)
1. \(20\) m
2. \(30\) m
3. \(10\) m
4. \(40\) m
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. | \(v_0 \cos \frac{\theta}{2}\) |
A projectile is projected with speed u at an angle of 30° with the vertical from the ground. The angle between the acceleration of the projectile and its velocity at the time of striking the horizontal ground is:
(1) 30°
(2) 60°
(3) 45°
(4) 0°
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 \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
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