Question

plzzzz solve it ........ ​

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

━━━━━━━━━━━━━━━━━━━━━

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

Step-by-step explanation:

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

$\red{\underline{\boxed{\bf{v=\dfrac{dx}{dt}}}}}$

Acceleration of a body 'a' is given by

$\green{\underline{\boxed{\bf{a=\dfrac{dv}{dt}}}}}$

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

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

So,

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