A particle moves along a straight line such that distance x traversed in t seconds is given by x = t2(t + 1), the acceleration of the particle, will be
3t3 - 2t
3t2 + 2t
6t - 2
6t + 2
Correct Answer :
D. 6t + 2
Related Questions
The angular speed of a car while taking a circular turn of radius 100 m at 36 km/hour, is
0.1 radian/sec
1 radian/sec
100 radian/sec
1000 radian/sec
Pick up the correct statement from the following:
Nature plays an important role in the launch of a satellite
The earth's gravity reduces the speed of a satellite by 32 km per second
The gravitational force relents as the satellite climbs higher
All the above
A uniform rod 9 m long weighing 40 kg is pivoted at a point 2 m from one end where a weight of 120 kg is suspended. The required force acting at the end in a direction perpendicular to rod to keep it equilibrium, at an inclination 60° with horizontal, is
40 kg
60 kg
10 kg
100 kg
The intrinsic equation of catenary is
S = c tan ψ
y = c cosh x/c
y = c cosh ψ
y = c sinh ψ
A smooth cylinder lying on its convex surface remains
In stable equilibrium
In unstable equilibrium
In neutral equilibrium
Out of equilibrium
If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to
7 kg
1 kg
5 kg
None of these
If a body is lying on a plane whose inclination with the horizontal is less than the angle of friction, then? (i) A force is required to move the body upwards (ii) A force is required to move the body downward (iii) The body will not be in equilibrium The correct answer is
Only (i)
Only (ii)
Both (i) and (ii)
Both (i) and (iii)
The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is
98 m
490 m
980 m
1960 m
A ball which is thrown upwards, returns to the ground describing a parabolic path during its flight
Vertical component of velocity remains constant
Horizontal component of velocity remains constant
Speed of the ball remains constant
Kinetic energy of the ball remains constant
A rigid body is in a stable equilibrium if the application of any force
Can raise the CG of the body but cannot lower it
Tends to lower the CG of the body
Neither raises nor lowers the CG of the body
None of above
A ladder of weight 'w' rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan'1 x, where x is
1/4
1/3
3
4
In simple harmonic motion, acceleration of a particle is proportional to
Rate of change of velocity
Displacement
Velocity
Direction
Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and
Concurrent
Parallel
Concurrent parallel
None of these
The load shared by the member BC of the structure shown in below figure is
23 t
32 t
4 t
3 t
At the instantaneous center, the velocity of the moving lamina at any instant is
Zero
Maximum
Minimum
Varying
Power developed by a torque, is
2πNT kg m/min
2πNT/4500 h.p
2πNT /60 watts
All the above
The graphical method of determining the forces in the members of a truss is based on
Method of joint
Method of section
Either method
None of the two methods
The diagram showing the point of application and line of action of forces in their plane is called
Vector diagram
Space diagram
Force diagram
Funicular diagram
Pick up the correct statement from the following for the structure shown in below figure.
The horizontal reaction at A is 2 √3t ←
The horizontal reaction at C is 2 √3t →
The vertical reaction at A is zero
All the above
The Centre of gravity of a 10 × 15 × 5 cm T-section from its bottom, is
7.5 cm
5.0 cm
8.75 cm
7.85 cm
The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
1 : 2
1 : 1
2 : 1
3 : 1
A body is dropped from a height of 100 m and at the same time another body is projected vertically upward with a velocity of 10 m/sec. The two particles will
Never meet
Meet after 1 sec
Meet after 5 sec
Meet after 10 sec
M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is
π/64 (D4 + d4)
π/32 (D4 - d4)
π/32 (D4 + d4)
π/32 (D4 × d4)
The maximum displacement of a particle executing S.H.M. corresponds to
Zero potential energy and maximum kinetic energy
Zero kinetic energy and maximum potential energy
Maximum kinetic energy and maximum potential energy
Minimum kinetic energy and minimum potential energy
Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by
5.5 kg
6.25 kg
8.75 kg
10.5 kg
The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be
30°
45°
60°
75°
The following factor affects the orbit of a satellite up to an altitude of 720 km from the earth's surface
Uneven distribution of the gravitational field
Gravity of the sun and the moon
Aerodynamic forces
None of these
The shape of a suspended cable under its own weight, is
Parabolic
Circular
Catenary
Elliptical
In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is
1.5
5
25
314
Varingons theorem of moments states
Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point