Question

A particle starts from origin. If velocity is
depending on time as v = t² - 6t. Find its position
at the moment acceleration is zero.

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Answer 1

Answer:

The particle is at 18 m when its acceleration is zero.

Explanation:

First we need to find the time when acceleration is zero

Given velocity as a function of time as

$v=t^2-6t$

Acceleration is nothing but rate of change of velocity

i.e. $a=\frac{dv}{dt}$

or, $a=\frac{d}{dt} (t^2-6t)}\\\implies a=2t-6$

When a = 0

2t - 6 = 0

⇒ t = 3 seconds

Since the particle starts from origin, at t = 0, s = 0

Also, rate of change of displacement is velocity

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

$\implies ds=vdt$

$\implies ds=(t^2-6t)dt$

$\implies \int_0^sds=\int_0^3(t^2-6t)dt$

$\implies s=\frac{t^3}{3}-3t^2\Bigr|_0^3$

$\implies s=9-27$

$\implies s=-18 \text{ m}$