A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (i) t⅟² (ii) t (iii) t³́² (iv) t²
The body starts from rest so,its initial velocity is zero.
The final velocity of the moving body is given as,
v = u + a t
where, v is the final velocityof the body, u is the initial velocityof the body, a is the acceleration with which the body is moving and t is the time taken.
By substitutingthe value of u in the above equation, we get
v = a t
The power delivered to the body is given as,
P = F v
where, F is the force experienced by the body which is calculatedbythe product of mass and acceleration of the body.
By substituting the value of Fand vin the above equation, we get
P = ( m a ) ( a t ) = m a 2 t
Since, the body is moving with a constant acceleration therefore,
P ∝ t
Thus, option (ii) is correct.
The body starts from rest so,its initial velocity is zero.
The final velocity of the moving body is given as,
where, v is the final velocityof the body, u is the initial velocityof the body, a is the acceleration with which the body is moving and t is the time taken.
By substitutingthe value of u in the above equation, we get
The power delivered to the body is given as,
where, F is the force experienced by the body which is calculatedbythe product of mass and acceleration of the body.
By substituting the value of Fand vin the above equation, we get
Since, the body is moving with a constant acceleration therefore,
Thus, option (ii) is correct.
