Question

A particle moves along x-axis in such a way that its coordinate (x) varies with time (t) according to the expression x = (2 –5t +6t2) metre. The initial velocity of the particle is

Answer 1

The initial velocity is -5 m/s

Given:

Equation of motion of a particle moving along x axis is given below:

$x = 2 - 5t + 6 {t}^{2}$

Solution:

The calculation of initial velocity is done by differentiating the displacement with time.  

Therefore differentiating the equation,

$v = \frac{dx}{dt } \\ = d \frac{2 - 5t + 6t {}^{2} }{dt} \\ = v = - 5 + 12$

Thereby,

For initial velocity, the time taken will be zero, thus, input value of time, t = 0

Initial velocity, v = -5 m/s

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