Question

The instantaneous velocity of a body, moving along

a straight line whose position is described by the

equation x=9+2t2 (in cm), at time 5 seconds will

be
​

Answer 1

Answer: 20 m/s

Explanation:

v = dx/dt

v = d/dt ( 9 + 2t^2 )

v = 4t

v = 4*5 ( since t =5 )

v = 20

Answer 2

Answer:

• The instantaneous velocity (v) is 20 m/s

Given:

1. Given relation:- x = 9 + 2 t²
2. Time taken (t) = 5 seconds.

Explanation:

$\rule{300}{1.5}$

From the relation we know,

x = 9 + 2 t²

Now, differentiating it to get velocity.

$\displaystyle\longrightarrow\sf x = 9 + 2\;t^{2}\\\\\\\longrightarrow\sf \dfrac{dx}{dt}=\dfrac{d\;(9+2\;t^{2})}{dt}\\\\\\\longrightarrow\sf v=0+(2\times 2)\;t^{\;(2-1)}\ \ \because \Bigg[v=\dfrac{dx}{dt}\Bigg]\\\\\\\longrightarrow\sf v=4\;t\\\\\\\longrightarrow \underline{\boxed{\sf v=4t\;m/s}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Now, Substituting time period t = 5 seconds

$\displaystyle\longrightarrow\sf v=4\;t\\\\\\\longrightarrow\sf v = 4\times 5 \ \ \because \bigg[t=5\;sec\bigg]\\\\\\\longrightarrow\sf v = 20\\\\\\\longrightarrow \large{\underline{\boxed{\red{\sf v=20\;m/s}}}}$

∴ The instantaneous velocity (v) is 20 m/s.

$\rule{300}{1.5}$