Question

The position x of a particle moving along a straight line path varies with time according to the relation x=6t square -5t,where x is in metre,t is in second. The initial velocity of the particle is

Answer 1

given X=6t^2-5t

u= dx/dt

u= d (6t^2-5t)/dt

u= 12t-5 m/s

Hope it would be helpful. ....
thank you

Answer 2

Here in this question, the position (X) of a particle is given as a function of time (t).

$X=6t^{2}-5t$ -------------(1)

We wanted to find a Velocity. So we need to have a function of velocity (V)

When the above equation (1) differentiate once by time you can obtain the function for velocity (V)

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

At the initial point t=0. When t=0,

$V=12X0-5\\\\V=-5ms^{-1}$