The position of a particle moving in the XY plane at any time t is given by x=(3t2−6t) metres. Select the correct statement about the moving particle from the following.
1. The acceleration of the particle is zero at t = 0 second
2. The velocity of the particle is zero at t = 0 second
3. The velocity of the particle is zero at t = 1 second
4. The velocity and acceleration of the particle are never zero
If body having initial velocity zero is moving with uniform acceleration 8 m/sec2 , then the distance travelled by it in fifth second will be
1. 36 metres
2. 40 metres
3. 100 metres
4. Zero
An alpha particle enters a hollow tube of 4 m length with an initial speed of 1 km/s. It is accelerated in the tube and comes out of it with a speed of 9 km/s. The time for which it remains inside the tube is
1. 8×10−3 s
2. 80×10−3s
3. 800×10−3s
4. 8×10−4s
Two cars A and B are travelling in the same direction with velocities v1 and v2(v1>v2). When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when:
1. d<(v1−v2)22a
2. d<v21−v222a
3. d>(v1−v2)22a
4. d>v21−v222a
A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 seconds on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is
1. 3 m/sec2
2. –3 m/sec2
3. 0.3 m/sec2
4. –0.3 m/sec2
A body starts from rest from the origin with an acceleration of 6 m/s2 along the x-axis and 8 m/s2 along the y-axis. Its distance from the origin after 4 seconds will be:
1. 56 m
2. 64 m
3. 80 m
4. 128 m
A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is 30 m/s, it can be stopped by this force in
1. 203m
2. 20 m
3. 60 m
4. 180 m
The displacement of a particle is given by y=a+bt+ct2−dt4. The initial velocity and acceleration are, respectively:
1. | b,−4d | 2. | −b,2c |
3. | b, 2c | 4. | 2c,−2d |
A car moving with a speed of 40 km/h can be stopped by applying brakes for atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance ?
1. 8 m
2. 2 m
3. 4 m
4. 6 m
An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 ms−2. 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:
1. √0.54 s
2. √6 s
3. 0.7 s
4. 1 s