Question

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

Answer 1

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

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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.

Answer 2

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.