Question

A particle is moving along X axis the position is given by
x = K + jt2where K = 8m and j = 4 m/s2 t is time. Find
velocity of particle at t = 0, t= 3 sec.

I don't know whether the question is correct or not but please help me..!! no spam...​

Answer 1

Given:

A particle is moving along X axis the position is given by x = k + jt² where k = 8m and j = 4 m/s² t is time.

To find:

Velocity of the object at t = 0sec and 3 sec.

Calculation:

Instantaneous velocity of any object can be calculated by differentiating the displacement function with respect to time.

$x = k + j {t}^{2}$

$= > v = \dfrac{dx}{dt}$

$= > v = \dfrac{d(k + j {t}^{2} )}{dt}$

$= > v = \dfrac{dk}{dt} + \dfrac{d( j {t}^{2} )}{dt}$

$= > v = \dfrac{dk}{dt} + j\dfrac{d( {t}^{2} )}{dt}$

$= > v = 0 + ( j \times 2t)$

$= > v = 2jt$

At time t = 0 sec ;

$= > v1 = (2 \times 4 \times 0) = 0 \: m {s}^{ - 1}$

At time t = 3 sec :

$= > v2= (2 \times 4 \times 3) = 24\: m {s}^{ - 1}$

So final answer is :

Velocity at 0 sec is zero and at 3 sec is 24 m/s.