A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of
A bullet emerge from a barrel of length 1.2 m with a speed of 640 ms-1 . Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is
The acceleration a (in ms-2 ) of a body, starting from rest varies with time t (in s) following the equation a = 3 t + 4. The velocity of the body at time t = 2 s will be
Figure below shows the distance-time graph of the motion of a car. It follows from the graph that the car is
in uniform motion
in non-uniform acceleration
A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. The fragments having equal masses fly off along mutually perpendicular direction with speed v. What will be the speed of the third (lighter) fragment ?
We can represent in the form of a figure as
Now if we use the conservation of momentum we get
o = (2m) v cos 45° + (2m) v cos 45° + mv1
So, v1 = − 4 cos 45° v = − , thus the velocity of the third part has a magnitude equal to , this makes an angle of 135° with respect to either of the three masses.
If a person can throw a stone to maximum height of h metre vertically, then the maximum distance through which it can be thrown horizontally by the same person is
A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
A particle is moving with a constant speed v in a circle. What is the magnitude of average velocity after half rotation ?
A box of mass 2 kg is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. Coefficient of static friction between the box and the roof of the car is 0.2 and g = 10 ms-2. This maximum acceleration of the car, for the box to remain stationary, is
A particle is travelling along a straight line OX. The distance x (in metre) of the particle from O at a time t is given by x = 37 + 27t − t3, where t is time in seconds. The distance of the particle from O when it comes to rest is