The magnitude of a vector $\overrightarrow{\mathrm{A}}$ is constant but it is changing its direction continuously. The angle between $\overrightarrow{\mathrm{A}}$ and $\frac{\mathrm{d}\overrightarrow{\mathrm{A}}}{\mathrm{dt}}$ is:

1. 180°

2. 120°

3. 90°

4. 0°

A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) $\mathrm{m}/{\mathrm{s}}^2$. What is the speed of the particle at the instant its x-coordinate is 84 m?

The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m $\stackrel{}{\mathrm{}}$
 where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:

A particle moves along a circle of radius \({{20}\over{\pi}} m\) with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. 40 ms^–2

2. 640π ms^–2

3. 160π ms^–2

4. 40π ms^–2

A particle (A) is dropped from a height and another particle (B) is projected in a horizontal direction with a speed of 5 m/s from the same height. The correct statement, from the following, is:

Two particles are projected with the same initial velocity, one makes an angle θ with the horizontal while the other makes an angle θ with the vertical. If their common range is R, then the product of their time of flight is directly proportional to:
1.  R
2.  $R^2$
3.  $\frac{1}{R}$
4.  $R^0$

Two particles are separated by a horizontal distance x as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. The time after which the horizontal distance between them becomes zero will be:
                     
1.  $\frac{x}{u}$

2.  $\frac{u}{2x}$

3.  $\frac{2u}{x}$

4.  None of the above

Two boys are standing at the ends \(A\) and \(B\) of the ground where \(AB =a.\) The boy at \(B\) starts running in a direction perpendicular to \(AB\) with velocity \(v_1.\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t,\) where \(t\) is:

A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) & \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?