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. \(2\sqrt{10}~\text{unit}\)
Two bodies of equal masses are projected, one from top of the tower in the horizontal direction and other from the foot of tower at an angle of 45° with the horizontal, then the acceleration of their center of mass is
(1) downward
(2) g downward
(3) downward
(4) upward
A projectile is projected at an angle of 60° from horizontal. At an instant, it is moving at an angle of 30° with horizontal with velocity 10 m/s. The radial acceleration of the particle at that instant is:
1.
2.
3.
4.
The initial velocity of a projectile is given by m/s. If acceleration due to gravity is g = 10() m/, then the time after which projectile returns to the same horizontal level is:
(1) 4 s
(2) 10 s
(3) 14 s
(4) 12 s
Two persons start moving along two crossroads with the same speed 5 m/s. One in the direction of north and other is in the direction of the east as shown in the figure. Angular velocity of A with respect to B is :
(1) 0.5 m/s
(2) Zero
(3) 1.0 m/s
(4) 2 m/s
In projectile motion, accelerations of the projectile when it is gaining height and losing height respectively are
(1) g upward, g upward
(2) g upward, g downward
(3) g downward, g downward
(4) g downward, g upward
A person, who can swim with speed \(u\) relative to water, wants to cross a river (of width \(d\) and water is flowing with speed \(v\)). The minimum time in which the person can do so is:
1. \(\frac{d}{v}\)
2. \(\frac{d}{u}\)
3. \(\frac{d}{\sqrt{v^{2} + u^{2}}}\)
4. \(\frac{d}{\sqrt{v^{2} - u^{2}}}\)
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