Question

find the time at which velocity of the object becomes zero x(t)=3t^2-4t​

Answer 1

Answer:

The required time is 2/3 sec

Explanation:

Given, x(t) = 3t² - 4t

Velocity is the rate of change of displacement of an object.

We get the velocity by differentiating the position of the object.

$\boxed{\longmapsto \sf v=\dfrac{dx}{dt}}$

Differentiating position,

$\implies \sf v=\dfrac{dx}{dt} \\\\ \implies \sf v=\dfrac{d}{dt}(3t^2-4t) \\\\ \implies \sf v=\dfrac{d}{dt}(3t^2)+\dfrac{d}{dt}(-4t) \\\\ \implies \sf v=6t-4$

So, the velocity = (6t - 4) m/s

Now, we have to find the time at which velocity of the object becomes zero.

Put v = 0,

⇒ v = 6t - 4

⇒ 0 = 6t - 4

⇒ 6t = 4

⇒ t = 4/6

⇒ t = 2/3 sec

Therefore, the required time is 2/3 sec