Displacement when $v=0$

Calculus Level 2

The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to time t by the equation $t=\sqrt{x}+3$ , where $x$ is in meters and $t$ is in seconds. Find the displacement of the particle when it's velocity is zero.

30m 12m 13.6m Zero

1 solution

Sparsh Sarode
May 15, 2016

$t=\sqrt{x}+3$

$\sqrt{x}=t-3$

$x=(t-3)^{2}$

$\frac{dx}{dt}=2(t-3)=0$

$t=3$

Substituting $t=3$ in the given equation,

$3=\sqrt{x}+3$

$x=0$

I think you should write $x = (t-3)^{2}$ instead $\sqrt{x} = t-3$ since the second statement implies $t \ge 3$

A Former Brilliant Member - 5 years, 1 month ago

Written it in 3rd step..

Sparsh Sarode - 5 years, 1 month ago

I meant in the question.

A Former Brilliant Member - 5 years, 1 month ago

@A Former Brilliant Member – Hmmm... How does it matter? The question just asks for the condition for the velocity to be 0

Sparsh Sarode - 5 years, 1 month ago

Displacement when v = 0 v=0 v = 0

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Displacement when $v=0$