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A scooter starting from rest moves with a constant acceleration for a time ∆t1, then with a constant velocity for the next ∆t2 and finally with a constant deceleration for the next ∆t3 to come to rest. A 500 N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is
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Two cars of unequal masses use similar tyres. If they are moving at the same initial speed, the minimum stopping distance
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In order to stop a car in shortest distance on a horizontal road, one should
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Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional force on the vehicle by the road
(a) is towards east if the vehicle is accelerating
(b) is zero if the vehicle is moving with a uniform velocity
(c) must be towards east
(d) must be towards west.
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A care is going at a speed of 21.6 km/hr when it encounters at 12.8 m long slope of angle 30° (in the following figure). The friction coefficient between the road and the tyre is `1/2sqrt3`. Show that no matter how hard the driver applies the brakes, the car will reach the bottom with a speed greater than 36 km/hr. Take g = 10 m/s2.

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A car starts from rest on a half kilometre long bridge. The coefficient of friction between the tyre and the road is 1.0. Show that one cannot drive through the bridge in less than 10 s.
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In a rotating body, \[\alpha = \alpha r\text{ and }\nu = \omega r.\] Thus \[\frac{\alpha}{\alpha} = \frac{\nu}{\omega}.\] Can you use the theorems of ration and proportion studied in algebra so as to write \[\frac{\alpha + \alpha}{\alpha - \alpha} = \frac{\nu + \omega}{\nu - \omega}\]
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Consider the following two equations
(A) \[L = I \omega\]
(B) \[\frac{dL}{dt} = \Gamma\]
In noninertial frames _______________ .
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A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
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A wheel starting from rest is uniformly accelerated at 4 rad/s2 for 10 seconds. It is allowed to rotate uniformly for the next 10 seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.
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A body rotates about a fixed axis with an angular acceleration of one radian/second. Through what angle does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.
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Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are v1 and v2 respectively.
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A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.
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At a metro station, a girl walks up a stationary escalator in time t1. If she remains stationary on the escalator, then the escalator take her up in time t2. The time taken by her to walk up on the moving escalator will be ______.
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For the one-dimensional motion, described by x = t – sint
- x (t) > 0 for all t > 0.
- v (t) > 0 for all t > 0.
- a (t) > 0 for all t > 0.
- v (t) lies between 0 and 2.
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A spring with one end attached to a mass and the other to a rigid support is stretched and released.
- Magnitude of acceleration, when just released is maximum.
- Magnitude of acceleration, when at equilibrium position, is maximum.
- Speed is maximum when mass is at equilibrium position.
- Magnitude of displacement is always maximum whenever speed is minimum.
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A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground ______.
- the direction of motion of the ball changes every 10 seconds.
- speed of ball changes every 10 seconds.
- average speed of ball over any 20 second interval is fixed.
- the acceleration of ball is the same as from the train.
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Give examples of a one-dimensional motion where
- the particle moving along positive x-direction comes to rest periodically and moves forward.
- the particle moving along positive x-direction comes to rest periodically and moves backward.
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A motor car moving at a speed of 72 km/h can not come to a stop in less than 3.0 s while for a truck this time interval is 5.0 s. On a highway the car is behind the truck both moving at 72 km/h. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it does not bump into (collide with) the truck. Human response time is 0.5 s.
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A particle falling vertically from a height hits a plane surface inclined to horizontal at an angle θ with speed vo and rebounds elastically (Figure). Find the distance along the plane where if will hit second time.

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