Question

23
A particle located at x = 0, at time t = 0, starts moving along the positive x-direction with a velocity
that
varies as v=px. The displacement of the particle varies with time as (where, p is constant)​

Answer 1

Given that,

Velocity of a particle varies as v=px

To find,

The variation of displacement wrt time t.

Solution,

Velocity of an object is :

$\dfrac{dx}{dt}=px\\\\\dfrac{dx}{x}=pdt$

Integrating both sides, we get :

$\int\limits^x_0 {\dfrac{dx}{x}}=\int\limits^t_0 {pdt}\\\\lnx=pt\\\\x=e^{pt}$

Therefore, x varies exponentionally.

Answer 2

Hola ⚘⚘

Given:

• Velocity of a particle varies as v = px

Tofind:

• The variation of displacement wrt time t.

Calculation:

Velocity of an object -

>> dx/dt = px

>> dx/x = pdt

Integrating both sides-

⠀⠀ₓ⠀⠀⠀⠀⠀ ₜ

>> ∫ dx/dt = ∫ pdt

⠀ ⁰⠀⠀⠀⠀⠀ ⁰

>> lnx = pt $\:$

>> x = eᵖᵗ

Hence, x varies exponentionally