A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity vv with time between the time t1t1 as it hits the bat and time t2t2 when it touches the ground:
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The xx and yy coordinates of the particle at any time are x=5t−2t2x=5t−2t2 and y=10ty=10t respectively, where xx and yy are in metres and tt is in seconds. The acceleration of the particle at t=2t=2 s is:
1. 00 m/s2
2. 55 m/s2
3. −4−4 m/s2
4. −8−8 m/s2
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2t2. The time taken by her to walk up on the moving escalator will be
1. t1-t22t1−t22
2. t1t2t2-t1t1t2t2−t1
3. t1t2t2+t1t1t2t2+t1
4. t1-t2t1−t2
A particle moves so that its position vector is given by r=cosωtˆx+sinωtˆyr=cosωt^x+sinωt^y where ωω is a constant. Based on the information given, which of the following is true?
1. | The velocity and acceleration, both are parallel to r.r. |
2. | The velocity is perpendicular to rr and acceleration is directed towards the origin. |
3. | The velocity is not perpendicular to rr and acceleration is directed away from the origin. |
4. | The velocity and acceleration, both are perpendicular to r.r. |
A particle of mass 10g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8x10-4 J by the end of the second revolution after the beginning of the motion?
1. 0.15 m/s2
2. 0.18 m/s2
3. 0.2 m/s2
4. 0.1 m/s2
A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle θθ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m/s2) is: [Given, g = 9.8 m/s2]
1. 3.5
2. 5.9
3. 16.3
4. 110.8
A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (vav) from t = 0 to t = 5s is
1. 1515(13ˆiˆi+14ˆjˆj)
2. 7373(ˆiˆi+ˆjˆj)
3. 2(ˆiˆi+ˆjˆj)
4. 115115(ˆiˆi+ˆjˆj)
The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is:
1. -2i+3j
2. -2i-3j
3. 2i-3j
4. 2i+3j
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
1. θ=tan-1(14)θ=tan−1(14)
2. θ=tan-1(4)θ=tan−1(4)
3. θ=tan-1(2)θ=tan−1(2)
4. θ=45°θ=45°
A particle has an initial velocity (2ˆi+3ˆj2^i+3^j) and an acceleration (0.3ˆi+0.2ˆj0.3^i+0.2^j). The magnitude of velocity after 1010 s will be:
1. 9√2 units9√2 units
2. 5√2 units5√2 units
3. 5 units5 units
4. 9 units9 units