Question

The potential energy (in joule) of a body of mass 2 kg moving in the x-y plane is given by
U=6x+8ywhere the position coordinates x and y are measured in metre. If the body is at rest at
point (6m, 4m) at time t=0, it will cross the y-axis at time t equal to​

Answer 1

The time will be 2 sec.

Explanation:

Given that,

Mass = 2 kg

The potential energy is

$U=6x+8y$

We need to calculate the force

Using potential energy

$F=-\dfrac{dU}{dx}-\dfrac{dU}{dy}$

Put the value into the formula

$F=-6i-8j$

We need to calculate acceleration along x axis

Using formula of acceleration

$a_{x}=\dfrac{F}{m}$

Put the value into the formula

$a_{x}=\dfrac{-6}{2}$

$a_{x}=-3\ m/s^2$

We need to calculate acceleration along x axis

Using formula of acceleration

$a_{y}=\dfrac{F}{m}$

Put the value into the formula

$a_{y}=\dfrac{-8}{2}$

$a_{y}=-4\ m/s^2$

When the particle cross the y axis then  x= 0

So, The displacement of the object is -6 m.

$x_{initial}=6\ m$

We need to calculate the time

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

Put the value into the formula

$6=0+\dfrac{1}{2}\times3\times t^2$

$t=2\ sec$

Hence, The time will be 2 sec.

Learn more :

Topic : potential energy

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Answer 2

Answer:

time = 2 seconds........