If a point moves in straight line in such a manner that its acceleration is proportional to its speed (a ∝ v) , what is the relation between distance covered and speed?
a) #x prop v#
b) #x prop v^2#
c) #x prop v^3#
d) #x prop sqrtv#
a)
b)
c)
d)
1 Answer
Dec 29, 2017
I get (a)
Explanation:
Given that acceleration
From definition of acceleration and velocity
Integrating both sides with time
#int(dv)/(dt)dt=v+c#
where#c# is a constant of integration and can be found from initial conditions.
For RHS we get
#intdx/dt dt=x+c_1#
where#c_1# is a constant of integration and can be found from initial conditions.
Assuming that initially at
#vpropx#
#=>xpropv#