Question

if the displacement x of a particle depends on time,t as x is equal to 3t^2+2t+5 then find the instantaneous velocity of particle at t is equal to 3 second.​

Answer 1

Answer:

Instantaneous velocity = 20 m/s

Step by step explanations :

given that,

the displacement x of a particle depends on time,t as x = 3t² + 2t + 5

here,

x = 3t² + 2t + 5

we know that,

instantaneous velocity =

$\large{ \frac{ \large{dx}}{ \large{dt}} }$

putting the value of x

$\large{ \frac{ \large{d3 {t}^{2} + 2t + 5 }}{ \large{dt}} }$

by differentiating we get,

$\large{6 {t}^{2} + 2 }$

here

we have,

v = 6t² + 2

now,

to find,

the instantaneous velocity

at t = 3 seconds

putting the value of t as 3

v = 6t² + 2

v = 6(3) + 2

v = 18 + 2

v = 20 m/s

so,

instantaneous velocity of particle at t = 3 second

= 20 m/s

Answer 2

Answer :-

v = 20 m/s

Given :-

$x = 3t^2 + 2t + 5$

t = 3s

To find :-

It's instantaneous velocity.

Solution:-

we know that the instantaneous velocity of the particle is given by :-

$\huge \boxed{V_{inst} = \lim{\Delta t \rightarrow 0 }\dfrac{\Delta x}{\Delta t} }$

→$V_{inst} = \dfrac{dx}{dt}$

Now,

→$V_{inst} = \dfrac{d(3t^2+2t+5)}{dt}$

$V_{inst} = 3 \times 2 t + 2 \times 1 + 0$

→$V_{inst} = 6t +2$

at t = 3s

→$V_{inst} = 6 \times 3 + 2$

→$V_{inst} = 18 + 2$

→$V_{inst} = 20 m/s$

hence,

The instantaneous velocity will be 20 m/s.