Finding Average Velocity

Q.

A boy goes to market at an average speed $29\mathrm{km}{\mathrm{h}}^{-1}$ Finding the market closed, he immediately returns back by the same path with an average speed of $40\mathrm{km}{\mathrm{h}}^{-1}$ If the boy covers half the path during his return journey, find the average speed and average velocity.

Q. A rubber ball is dropped from a height of 5 m on a plane, where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of (1)3/5 (2)2/5 (3)16/25 (4)9/2

Q.

The displacement of a particle of mass 1 kg on a horizontal smooth surface is a function of time given by

$x=\frac{1}{3}{t}^3$. Find out the work done by the external agent for the first one second.

1. 1 Joules

2. 2 Joules

3. 0.5 Joules

4. None of these

Q. Speed of a particle moving on a circular path of radius 2m is varying with time as v=(2t^)m/s. Net acceleration of the particle at t=2s is 8√n m/s^2. The value of n is

Q. A particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The average velocity of the particle is

1. $2\pi m{s}^{-1}$
2. $4\pi m{s}^{-1}$
3. $2m{s}^{-1}$
4. $4m{s}^{-1}$

Q.

A ball is dropped from a height $h_0$ on a horizontal floor and keeps rebounding after hitting the floor. Find: (i) speed after $n$ rebounds

(ii) Total distance travelled by the ball before stopping

(iii) Height it rises after nth rebound

(iv) Total time before stopping

(coefficient of restitution is $e$)

1. (i) , (ii), (iii) , (iv)

2. (i) , (ii), (iii) , (iv)

3. (i), (ii), (iii)infinite (iv) infinite

4. None of these

Q. how force is equal to density× area× velocity^{

Q. a solid sphere of mass m is rolling with speed v on a horizontal surface and strikes a massless spring of forces cons†an t k then the maximum compression in the spring is?

Q. A particle moves in a circle of radius 5cm with cons†an t speed and time period 0.2pi seconds.The acceleration of the particle is options:1)5m/sec2 2)15 m/sec2 3)25m/sec2 4)36m/sec

Q. 32A disc of mass 1-0 kg is kept floating horizontally inair by firing bullets of mass 0-05 kg each verticallyat it, at the rate of 10 per second. If the bulletsrebound with the same speed, the speed with which99 these are fired will be-IGSAFV.dn) ueselV95dtMg(2) 0.98 m/s(4) 98-0 m/s(1) 0.098 m/s(3) 9.8 m/sntationary

Q. A balloon rises upward with speed of
10 m/s when the balloon is at a height of 100 m above ground a stone is dropped from it.
a) Time taken by stone to reach ground.
b) Maximum height attained by stone.

Q. The magnitude of change in velocity of a particle having speed v is v during a time interval delta t while moving in a uniform circular motion. The magnitude of average force on the particle is proportio nal to

Q. Two identical drops falling with a terminal speed 'v' coalesce to form a bigger drop. The terminal velocity of the bigger drop will be

1. 
2. 
3. 
4. 

Q.

A body is moving on a circle of radius of 80 m with a speed 20 m/s which is decreasing at the rate of 5 m/$s^2$ at an instant. The angle made by its acceleration with its velocity is

Q. 94.A projectile has a maximum range of 16 km.At the highest point of its motion, it explodes into two equal masses.One mass drops vertically downward the horizontal distance covered by the other mass from the time of explosion is?

Q. two boys start running towards each other from two points they are 120 m apart one runs with a speed of 5m/s and other with a speed of 7 m/s .When and where do they meet each other from 1st poin

Q. 35. A particle of mass 200 g, is whirled into a verticalcircle of radius 80 cm using a massless stringThe speed of the particle when the string makesan angle of 60^° with the vertical line is 1.5 msThe tension in the string at this position is(1) 1 N(2) 1.56 N(3) 2 N(4) 3 Nmass 1 ka is tied with a stringand

Q.

A body covers the first half of the distance with a velocity v and the second half in double the time taken for the first half. The average velocity is

1. $v$

2. $\frac{v}{2}$

3. $\frac{2v}{3}$

4. $\frac{2}{3v}$

Q. Two particles of equal mass are connected to a rope AB ofnegligible mass, such that one is at end A and the other dividing the length of the rope in the ratio 1:2 from A. The rope is rotated about end B in a horizontal plane. Ratio of the tensions in the smaller part to the other is (ignore effect ofgravity)(a) 4:3 (b) 1:4(c) 1:2(d) 1:

Q. 1. A boy standing near the edge of a cliff 125m above a river throws astone downward with a speed of 10m/s.find A) with what speed will the stone hit water

Q. A stone of mass m, tied to the end of a string, is whirled areund in a horizontal circle.(Negleet the force due to gravity). The lengththe string is reduced gradually, keepingthe angular momentum of the stone about thecentre of the circle constant. If the tension inthe string is given by T- Ar^{}, where a is aconstant, r is, the instantaneous radius of thecircle, then the value of a n is

Q. 38.A mass of 10g moving horizontally with a velocity of 100cm/s strikes a pendulum bob of mass 10g length of string is 50cm. The two masses stick together. The maximum height reached by the string now is (g=10m/s square) (1)7.5cm (2)5cm (3)2.5cm (4)1.25cm

Q. A stone of mass 1kg tied to a light string of length l=10m is whirling in a circular path in the vertical plane. if the ratio of the maximum to minimum tensions in the string is 3, find the speeds of the stone at lowest and highest points.

Q. The equation of path of a particle, projected obliquely from the ground under gravity is given by y=2x-x^2, where x and y are in metre. the x and y axes are in horizontal and vertical directions respectively. The speed of projection is (1)2.5m/s (2)5m/s (3)10m/s (4)20m/s.

Q. If a body is moving uniformly on a circle with speed v, then the magnitude of change in its velocity when it has turned by an angle theta is

Q. The acceleration-time graph of a body moving with uniform retardation is a straight line parallel to time axis, then

Q. a stone is thrown downwards with velocity 10m/s from the roof of a building and it reaches the ground with speed 40m/s .the height of the building

Q. A body falling from rest describes distances S1, S2 and S3 is the 1st , 2nd and 3rd seconds of its fall . Then the ratio of S1:S2:S3 A) 1:1:1 B) 1:3:5 C) 1:2:3 D) 1:4:9

Q. 82.A car move on a circular path of radius 5m At one instant the speed of car is 5m/s and it is decreased at a rate of 5m/s2 the angle between acceleration vector and velocity vector at this instat is

Q. 43.A balloon is rising vertically up with a constant speed 10 m/s. A stone is dropped from it when the ballon is at height 40 m . total distance covered by the stone before reaching the ground is 50 m 60 m 40 m 45 m