The acceleration of a body moving along x-axis depends on time as a^{1/2} ∝ t .(Initially the particle is at rest ) The velocity of body is proportional to time t as??
Answers
Answered by
3
Given : The acceleration of a body moving along x-axis depends on time as a^{1/2} ∝ t .
(Initially the particle is at rest )
To Find : The velocity of body is proportional to time t as
Solution:
a^{1/2} ∝ t .
=> √a ∝ t
Squaring both sides
=> a ∝ t²
=> a = kt²
where k is some constant
a = dv/dt
=> dv/dt = kt²
=> dv = kt²dt
integrating both sides
∫ dv = ∫ kt²dt
=> v = kt³/3 + c
at t = 0 , v = 0
=> 0 = 0 + c
=> c = 0
Hence v = kt³/3
=> v = (k/3)t³
(k/3) is constant
Hence v ∝ t³
The velocity of body is proportional to time t as cube
Learn More:
A particle is dropped from a height of 80m . Find the distance ...
brainly.in/question/11370407
A ball is dropped from a height of 80ft the ball is such that it ...
brainly.in/question/11471174
Similar questions