# 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

#### Answer:

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#