A particle has an initial velocity $\overrightarrow{\mathrm{u}}=(4\hat{i}-5\hat{j})$ m/s and it is moving with an acceleration $\overrightarrow{\mathrm{a}}=\left(\frac{1}{4}\hat{i}+\frac{1}{5}\hat{j}\right)m/s^2$. Velocity of the particle at \(t=2\) s will be:

1. $(6\hat{\mathrm{i}}-4\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

2. $(4.5\hat{i}-4.5\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

3. $(4.5\hat{i}-4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

4. $(6\hat{\mathrm{i}}-4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

A body is projected with a velocity of $(3\hat{i}+4\hat{j})m/s$. The maximum height attained by the projectile is (g = 10 ms^–2)

Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1.  $A>B>C$

2. $C>A>B$

3. $B>A>C$

4. $A=B=C$

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella? [Given: tan 16º = 0.29 & tan 18º = 0.33]

1. 16º with the vertical, towards north

2. 18º with the vertical, towards north

3. 16º with the vertical, towards south

4. 18º with the vertical, towards south

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle at a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of the acceleration of the stone?
1. 8.1 ms^-2
2. 7.7 ms^-2
3. 8.7 ms^-2
4. 9.9 ms^-2

A particle starts from the origin at t = 0 sec with a velocity of $10$ $\hat{j}$ $m/s$ and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?

A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of \(|displacement| \over distance\) will be:
1. 0
2. 1/7
3. 2/7
4. 1/11

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of 5 m/s at an angle of \(120^\circ\) with the flow. The speed of the flow must be:
1. \(2.5\) m/s
2. \(3\) m/s
3. \(4\) m/s
4. \(1.5\) m/s

A car with a vertical windshield moves in a rain storm at a speed of \(40\) km/hr. The rain drops fall vertically with a constant speed of \(20\) m/s. The angle at which raindrops strike the windshield is:
1. ${\tan }^{-1}\frac{5}{9}$

2. ${\tan }^{-1}\frac{9}{5}$

3. ${\tan }^{-1}\frac{3}{2}$

4. ${\tan }^{-1}\frac{2}{3}$