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Important Problem and Solution Part 1 on Kinematics


Question 1
A particle moves in a straight line according to the relation
x=t3-4t2+3t
Find the acceleration of the particle at displacement equal to zero.
  1. (-8,-2,-10)
  2. (-1,-2,10)
  3. (8,2,10)
  4. (1,2,10)
Question 2
A body starts at initial velocity v0 in a straight line with acceleration as shown below in the graph.
/p> Find the maximum velocity reached.
  1. v0+4at0
  2. v0+9/2(at0)
  3. v0-9/2(at0)
  4. v0-4at0
Question 3
A particle moves in a straight line with acceleration described by equation given below
a=mx-(v02/x0)
If the initial velocity and displacement are (v0, 0) and at any time t0 velocity and displacement are (0, x0) the value of constant m is
/p> Question 4
The radius vector of point x relative to origin varies with time as
r=a cos(kt)i+b sin(kt)j
Where a and b are constants and i and j are vectors along x and y axis. Which one of the following is the mean velocity vector?
  1. [a cos(kt)i - b sin(kt)j]/t
  2. [a cos(kt)i + b sin(kt)j]
  3. [a cos(kt)i - b sin(kt)j]
  4. [a cos(kt)I +b sin(kt)j]/t
Question 5
A boat moves with the stream of water from point A and B and it return back with the same speed. Velocity of boat relative to water is  times the velocity of the water. Velocity of the water is 1m/sec. Find out the average speed in the whole ternary
/p> Question 6
A body is freely falling under the action of gravity. It covers half the total distance in the last second of its fall. If it falls for n second, then value of n is
  1. 2
  2. 2+√2
  3. 3
  4. (4) 2-√2
Question 7
/p> Two particle A and B start with the same velocity v=v0 at x=0.They are accelerated per the graph shown above. Which particle has the maximum magnitude of the velocity at x=x0
a. A
b. B
c. A & B will have same velocity
d. None of the above
Question 8
Distance and displacement of a moving object have same magnitude when
  1. When object moves in circular motion
  2. When object moves along a zig-zag path
  3. When object moves along straight line and always moves along  the same direction
  4. When it moves along straight line but the distance is not always same
Question 9
A wind is blowing in the North direction at the speed of 5 km/hr. An airplane moves to a point in the East which is 2000 km away in 40 hr. Find the velocity of the airplane  with respect to the wind.
/p> Question 10
Two projectile A and B are having trajectory equation
y=a1x-b1x2 and y=a2x-b2x2
If the range is same for both the projectile A and B then which of the following option is true
/p> Question 11
The greatest possible acceleration or deceleration a train may have is a and its maximum speed is v. Find the maximum time in which the train can get from one station to the next if the total distance is s
/p> Question 12
When the projectile is at the highest point of its trajectory, the direction of its velocity and acceleration are
a. parallel to each other
b. anti parallel to each other
c. Inclined to each other at 45
d. Perpendicular to each other

Question 13
The horizontal and vertical displacement of the projectile at time t are
x=36t
y=48t-4.9t2
where x and y are in meters and t in second. Initial velocity of the projectile in m/s
a. 15
c. 30
b. 45
d. 60

Question 14
Displacement(y) of the particle is given by
y=2t+t2-2t3
the velocity of the particle when acceleration is zero is given by
a. 5/2
b. 9/4
c. 13/6
d. 17/8

 Question 15
It is possible to project an body with a given speed in two possible ways so that it has a same horizontal range. The product of time taken by it in tow possible ways is
a. R/g
b. 2R/g
c. 3R/g
d. 4R/g

Question 16
A projectile has a range R and time of flight T. If the range is tripled by the increasing the speed of the projection, without changing the angle of projection then the time of the flight will become
a T/√3
b T√3
c. T/3
d. 3T

Question 17
A large number of stones are fired in all the direction with same speed V.The maximum area of the ground on which this stone will spread is
a. πV4/g2
b. π2V4/g2
c. πV4/g
d. πV/g2

Question 18
A body is projected horizontally from the top of the building 39.2 m high. How long will it take to hit the ground
a. 2 sec
b. 4 sec
c. 1 sec
d. 2√2 sec
Question 19
Three particles of mass m1,m2,m3 moves in plane with initial velocity v, v2 , v3 . A constant acceleration a acts on the three particles. At t=t0, there velocities becomes , . Which of the following expression are correct?
/p> Question 20
A particle is set in motion at t=0 such that velocity varies as  where v0 is a positive constant. Find the distance, displacement covered by the particle in first 3 sec
/p>
Question 21
Two cars A and B run at constant speed u1 and u2 along the highways intersecting at an angle θ. They start at t=0 at the intersection point. Find the time required to have distance s between the two cars
/p> Question 22
 A boy throws a ball with such an initial velocity and at such an angle of elevation, so that the range is r and maximum height to which ball rises is h. find the maximum range that can be obtained with same initial velocity
/p> Question 23
An airplane is moving with a horizontal velocity v at a height h above a level plane.If a projectile is fired from an gun at an instant when the plane is vertically above the gun, what is the minimum initial velocity of the projectile in order to hit the plane.
/p> Question 24
/p> A bar XY of length l which always remains in the same vertical plane has its ends X and Y constrained to remain in contact with the horizontal floor and in vertical wall as shown below in the figure.
The bar starts from a vertical position and end X is moved along the floor with a constant velocity v0 so that its displacement OX=v0t. The displacement time graph for Y end is
(a) Ellipse
(b) Circle
(c) Parabola
(d) Straight line
Question 25
An aero plane is moving in the sky and a bag is dropped from t he plane. Let a and v denote the acceleration and velocity of the aero plane. Consider two cases
  1. a is constant and non zero
  2. a is zero and plane is moving with uniform velocity
Match the following:-
(P) The trajectory of bag in case A w.r.t. ground is
(L) Parabola
(Q) The trajectory of bag in case B w.r.t. plane is
(M) straight line
(R) The trajectory of bag in case B w.r.t. ground is
(N) no appropriate match
(S) The trajectory of bag in case A w.r.t. plane is
(O) Circle
Question 26
The velocity, displacement, acceleration of a particle in one dimensional motion is given as
v1,x1,a at t=t0
v2,x2,a at t=t0 +?t
which of the following is correct
/p> Question 27
The displacement time equation for a particle in linear motion is given as
/p> which of the following option is correct
a)   The velocity and acceleration of the particle at t=0 is a and –ab respectively
b) The velocity will be decreasing as the time increases
c) The displacement of the particle will fall between
/p> d) The maximum acceleration in the motion is –ab
Question 28
An object under goes an projectile motion starting from origin with initial velocity
Under acceleration due to gravity
Hm  -> Maximum height reached by object
R -> Range of the object
Match the column
Column A
Column B
A) tan of angle between velocity and x axis at any point of time
/p>
B) tan of projection angle θ0 for a projectile at origin
/p>
C) Range of the projectile
/p>
D) tan of the angle of position vector at any time
/p>
/p>
Answers
  1. (a)
  2. (b)
  3. (a)
  4. (d)
  5. (a)
  6. (b)
  7. (b)
  8. (c)
  9. (c)
  10. (a)
  11. (b)
  12. (d)
  13. (d)
  14. (c)
  15. (b)
  16. (b)
  17. (a)
  18. (d)
  19. (d)
  20. (d)
  21. (c)
  22. (b)
  23. (a)
  24. (a)
  25. (P)—(L) ; (Q)—(M); (R)—(L); (S)—(M)
  26. (b),(c)
  27. (a),(b),(c),(d)
  28. (A)—(T);(B)—(S);(C)—(P);(D)—(Q)



Solutions

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