Question

The displacement of a particle in straight line is given by x =2t² + t + 5, where x is expressed in metres and t in seconds. Find the velocity of the particle at t =2sec.

Answer 1

Velocity : It is defined as displacement covered per unit time

Instantaneous Velocity : It is denoted as velocity at particular instant of time

$\pink{\bigstar}\ \; \sf v=\dfrac{dx}{dt}$

_____________________________________

Displacement of the particle in a straight line ,

➠  x = 2t² + t + 5

where ,

• x is in meters
• t is in seconds

Velocity of the particle is given by ,

$\to \sf v=\dfrac{dx}{dt}$

$\to \sf v=\dfrac{d}{dt}(2t^2+t+5)$

$\to \sf v=2(2t)+(1)+0$

$\to \sf \blue{v=4t+1}\ \; \bigstar$

Velocity of the particle at t = 2 s is ,

➠ v = 4(2) + 1

➠ v = 8 + 1

➠ v = 9 m/s  $\orange{\bigstar}$

Answer 2

Explanation:

Velocity : It is defined as displacement covered per unit time

Instantaneous Velocity : It is denoted as velocity at particular instant of time

\pink{\bigstar}\ \; \sf v=\dfrac{dx}{dt}★ v=

dt

dx

_____________________________________

Displacement of the particle in a straight line ,

➠ x = 2t² + t + 5

where ,

x is in meters

t is in seconds

Velocity of the particle is given by ,

\to \sf v=\dfrac{dx}{dt}→v=

dt

dx

\to \sf v=\dfrac{d}{dt}(2t^2+t+5)→v=

dt

d

(2t

2

+t+5)

\to \sf v=2(2t)+(1)+0→v=2(2t)+(1)+0

\to \sf \blue{v=4t+1}\ \; \bigstar→v=4t+1 ★

Velocity of the particle at t = 2 s is ,

➠ v = 4(2) + 1

➠ v = 8 + 1

➠ v = 9 m/s \orange{\bigstar}★