If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?
1. \(90^\circ\)
2. \(45^\circ\)
3. \(180^\circ\)
4. \(0^\circ\)

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:
              

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
1. $\theta ={\tan }^{-1}\left(\frac{1}{4}\right)$
2. $\theta ={\tan }^{-1}\left(4\right)$
3. $\theta ={\tan }^{-1}\left(2\right)$
4. $\theta ={45}^0$

A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

A body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) m/s towards the north. The average acceleration of the body is:
1. \( 7 \mathrm{~m} / \mathrm{s}^2 \)
2. \( \sqrt{7} \mathrm{~m} / \mathrm{s}^2 \)
3. \( 5 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1 \mathrm{~m} / \mathrm{s}^2\)

A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are ($\sqrt{3}$, \(3\)). The path of the particle makes an angle of __________ with the x-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

A car turns at a constant speed on a circular track of radius \(100\) m, taking \(62.8\) s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

A particle moves in space such that:
\(x=2t^3+3t+4;~y=t^2+4t-1;~z=2sin\pi t\)
where \(x,~y,~z\)  are measured in meters and \(t\) in seconds. The acceleration of the particle at \(t=3\) seconds will be:

A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\)  \((6\) m, \(7\) m) at time \(t=2\) s and   \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:

A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)$\stackrel{}{\mathrm{}}$) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m