Which of the following statements is incorrect?
1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
A man is walking on a horizontal road with a speed of \(4\) km/h. Suddenly, the rain starts vertically downwards with a speed of \(7\) km/h. The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}\) km/h
2. \(\sqrt{65}\) km/h
3. \(8\) km/h
4. \(4\) km/h
A particle of mass 6 kg moves with an initial velocity of m/s. A constant force of N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, when its y-coordinate again becomes zero is given by
(1) 6.0 m
(2) 12.8 m
(3) 8 m
(4) 25.6 m
In a uniform circular motion:
(1) Velocity and acceleration remain constant.
(2) Kinetic energy remains constant.
(3) Speed and acceleration changes.
(4) Only velocity changes, acceleration remains constant.
If a body is accelerating, then:
1. | it must speed up. |
2. | it may move at the same speed. |
3. | it may move with the same velocity. |
4. | it must slow down. |
Compared to an ideal projectile motion under gravity, which of the following is incorrect regarding another projectile motion in which air-friction is also considered?
(1) Time of flight decreases.
(2) The decrease in the horizontal component of velocity continuously.
(3) Angle with horizontal is less at the time of striking the ground compared to the angle of projection with horizontal.
(4) Angle with vertical is less at the time of striking the ground with respect to the angle of projection with vertical.
Two balls are projected to acquire same range with the same initial speed u but at different angles of projection. If maximum height acquired by balls are , then () is: (angle of projection of one projectile is )
(1)
(2)
(3)
(4) tan
At the highest point of trajectory in the ground to the ground projectile, the angle between gravitational acceleration and momentum is
(1) 30°
(2) 45°
(3) 90°
(4) Data insufficient
A particle revolves in a horizontal circle with decreasing velocity. The angle between instantaneous velocity and instantaneous acceleration of the particle at an instant is
(1) < 90°
(2) > 90°
(3) = 90°
(4) 90°