Question

→ Find velocity at, t = 5 sec

Motion of particle is given by
$\sf\:x(t)=4t^2+8t$m​

Answer 1

$\dag\:\underline{\sf AnsWer :}$

We are given that,the motion of particle is given by :

• x(t) = 4t² + 8t m

And we have to find the Velocity (v).

$\bigstar\:\underline{\textbf{According to the Question Now :}}$

$\dashrightarrow\:\sf Velocity = \dfrac{Displacement}{Time}$

On differentiating with respect to t, we get :

$\dashrightarrow\:\sf v = \dfrac{dx}{dt}$

$\dashrightarrow\:\sf v = \dfrac{d}{dt}( {4t}^{2} + 8t)$

$\bigstar\:\sf Rule = \dfrac{dx}{dt} = nx^{n-1}$

$\dashrightarrow\:\sf v = 2 \times {4t}^{(2 - 1)} + 8$

$\dashrightarrow\:\sf v = 8t + 8$

Now, we are also given that t = 5.

$\dashrightarrow\:\sf v = 8(5)+ 8$

$\dashrightarrow\:\sf v = 40+ 8$

$\dashrightarrow\: \underline{ \boxed{\sf v = 48 \:m/s}}$

Hence,the Velocity (v) of the given particle is 48 m/s.