Question

The displacement s of a particle at a time t is given by s = 2t³ -5t² + 4t - 3, find the velocity and the displacement at that time.

Answer 1

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Answer 2

Answer:

$v=6t^{2}-10t+4$

Step-by-step explanation:

In the question,

The displacement "s" of a particle is given by,

$s=2t^{3}-5t^{2}+4t-3$

So, as we know that the velocity 'v' of a particle is given by,

$v=\frac{ds}{dt}$

Therefore, on differentiating the displacement 's' w.r.t time (t) is given by,

$s=2t^{3}-5t^{2}+4t-3So,\\\frac{ds}{dt}=\frac{d}{dt}(2t^{3}-5t^{2}+4t-3)\\\frac{ds}{dt}=6t^{2}-10t+4$

So,

$v=6t^{2}-10t+4$

Therefore, the equation of the velocity w.r.t time, t is given by,

$v=6t^{2}-10t+4$

Here, the velocity of the function at any time 't' can be found out by putting the value of time, t in the equation.