(ii) t
Mass of the body = m
Acceleration of the body = a
Using Newton’s second law of motion, the force experienced by the body is given by the equation:
F = ma
Both m and a are constants. Hence, force F will also be constant.
F= ma = Constant … (i)
For velocity v, acceleration is given as, a = dv / dt = constant
dv = Constant × dt
v = at ....(ii)
Where, a is another constant
v ∝ t ...(iii)
Power is given by the relation: P = F.v
Using equations (i) and (iii), we have: p ∝ t
Hence, power is directly proportional to time.
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between \( t = 0 \) to \( t = 4s \)?
Find the mean and variance for the following frequency distribution.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
W = Force × Distance
Where,
Work (W) is equal to the force (f) time the distance.
W = F d Cos θ
Where,
W = Amount of work, F = Vector of force, D = Magnitude of displacement, and θ = Angle between the vector of force and vector of displacement.
The SI unit for the work is the joule (J), and it is defined as the work done by a force of 1 Newton in moving an object for a distance of one unit meter in the direction of the force.
Work formula is used to measure the amount of work done, force, or displacement in any maths or real-life problem. It is written as in Newton meter or Nm.