If the position of a particle varies according to the equations \(x= 3t^2\), \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?
1. | Velocities in \(y\) and \(z\) directions are constant |
2. | Acceleration in the \(x\text-\)direction is non-uniform |
3. | Acceleration in the \(x\text-\)direction is uniform |
4. | Motion is not in a straight line |
If three coordinates of a particle change according to the equations \(x = 3 t^{2}, y = 2 t , z= 4\), then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. \(2\sqrt{11}~\text{unit}\)
2. \(\sqrt{34}~\text{unit}\)
3. \(40~\text{unit}\)
4. \(2\sqrt{10}~\text{unit}\)
In a uniform circular motion, if the speed of the particle is \(2\) m/s and radius of the circle is \(2\) m, then the values of centripetal and tangential acceleration are, respectively:
1. \(2~\text{m/s}^2,~2~\text{m/s}^2\)
2. \(2~\text{m/s}^2,~1~\text{m/s}^2\)
3. \(0,~2~\text{m/s}^2\)
4. \(2~\text{m/s}^2,~0\)
The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero
Coordinates of a particle as a function of time \(t\) are \(x= 2t\),
\(y =4t\). It can be inferred that the path of the particle will be:
1. | Straight line
|
2. | Ellipse
|
3. | Parabola
|
4. | Hyperbola |
Which of the following statement/s is/are incorrect regarding the motion in a plane?
1. | a body can't move on a curved path with constant acceleration. |
2. | the angle between acceleration and velocity can be \(90^\circ.\) |
3. | the angle between acceleration and velocity can be other than \(90^\circ.\) |
4. | all of the above. |
A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s2 along the north. The velocity of the body just after \(4\) s will be?
1. | \(8\) m/s along East. |
2. | \(4 \sqrt{2} \) m/s along North-East. |
3. | \(8\) m/s along North. |
4. | \(4 \sqrt{2} \) m/s along South-East. |
A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s
1. | parallel to the position vector. |
2. | at \(60^{\circ}\) with position vector. |
3. | parallel to the acceleration vector. |
4. | perpendicular to the position vector. |
A projectile is projected from the ground with the velocity \(v_{0}\) at an angle \(\theta\) with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?
1. \(\sqrt{3} v_{0}\cos\theta\)
2. \(\frac{v_{0}}{\sqrt{2}} \sin\theta\)
3. \(\frac{v_{0}}{\sqrt{2}} \cos \theta\)
4. \(\sqrt{5} v_{0}\)