Physics, asked by neelg8218, 7 months ago

position of an object moving in x-y plane is given by r=(3t²i+2tj)m . acceleration of object at t=2 sec​

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Answered by Rohit18Bhadauria
19

Given:

Position of an object moving in x-y plane, r=(3t²i+2tj)m

To Find:

Acceleration of the object(particle) at t=2s

Solution:

We know that,

  • Velocity of a body 'v' is given by

\pink{\underline{\boxed{\bf{v=\dfrac{dx}{dt}}}}}

  • Acceleration of a body 'a' is given by

\purple{\underline{\boxed{\bf{a=\dfrac{dv}{dt}}}}}

where,

x is the displacement or position of particle at time t

━━━━━━━━━━━━━━━━━━━━━

Let the velocity of given particle be v and acceleration of given particle be a

So,

\longrightarrow\rm{\overrightarrow{v}=\dfrac{d\overrightarrow{r}}{dt}}

\longrightarrow\rm{\overrightarrow{v}=\dfrac{d(3t^{2}\hat{i}+2t\hat{j})}{dt}}

\longrightarrow\rm{\overrightarrow{v}=3(2t)\hat{i}+2(1)\hat{j}}

\longrightarrow\rm{\overrightarrow{v}=6t\hat{i}+2\hat{j}}

Also,

\longrightarrow\rm{\overrightarrow{a}=\dfrac{d\overrightarrow{v}}{dt}}

\longrightarrow\rm{\overrightarrow{a}=\dfrac{d(6t\hat{i}+2\hat{j})}{dt}}

\longrightarrow\rm{\overrightarrow{a}=6(1)\hat{i}+0\hat{j}}

\longrightarrow\rm{\overrightarrow{a}=6\hat{i}}

At t=2 s

\longrightarrow\rm\green{\overrightarrow{a}=6\hat{i}}

So,

Acceleration of given object is 6 m/s² in the direction of x-axis.


amitkumar44481: Perfect :-)
Answered by Anonymous
55

Answer:

Given:

  • Position of an object moving in x-y plane is given by r=(3t²i+2tj)m.

Find:

  • Acceleration of object at t=2 sec is.

Calculations:

  • Moving object: r = 3t² + 2t
  • Velocity: dx/dt

Using above values, we get:

⇢ d(3t² + 2t)/dt

⇢ v = 6t + 2

⇢ a = dv/dt

⇢ d(6 + 0)/dt²

⇢ a = 6 m/s²

Therefore, acceleration is 6 m/s².

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