Question

At time t = 0 a particle starts travelling from a height. 7 ${\displaystyle \hat{\text{z}}}$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the ${\displaystyle \hat{x}}$ and ${\displaystyle \hat{\text{y}}}$ directions are defined as 3t and 5t³ respectively, At t = 1s acceleration of the particle will be ______.

विकल्प

• -30 ${\displaystyle \hat{\text{y}}}$

• 30 ${\displaystyle \hat{\text{y}}}$

• ${\displaystyle 3\hat{x}+15\hat{\text{y}}}$

• ${\displaystyle 3\hat{x}+15\hat{\text{y}}+7\hat{\text{z}}}$

Answer 1

At time t = 0 a particle starts travelling from a height. 7 ${\displaystyle \hat{\text{z}}}$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the ${\displaystyle \hat{x}}$ and ${\displaystyle \hat{\text{y}}}$ directions are defined as 3t and 5t³ respectively, At t = 1s acceleration of the particle will be 30 `hat"y"`.

Explanation:

We have, ${\displaystyle \overrightarrow{\text{r}}=3\text{t}\hat{\text{i}}+5{\text{t}}^3\hat{\text{j}}+7\text{k}}$

So, ${\displaystyle \frac{{\text{d}}^2 \overrightarrow{\text{r}}}{{\text{dt}}^2}}$ = 30 t ${\displaystyle \hat{\text{j}}}$

At t = 1 ⇒

${\displaystyle \frac{{\text{d}}^2 \overrightarrow{\text{r}}}{{\text{dt}}^2}=30\hat{\text{j}}}$

⇒ ${\displaystyle \overrightarrow{\text{a}}=30\hat{\text{j}}}$