Question

5.
as
Given the position
of a particle
x = 12 + 2+ + 2 m, the average velocity
between
Os and 2s is
a) 10 m/s b) 4 m/s
c) 8 m/s
d) 6m/s

Answer 1

Question :

Given the position of a particle as x = t² + 2t + 2 m, the average velocity between 0s and 2s is

A) 10 m/s

B) 4 m/s

C) 8 m/s

D) 6 m/s

Given :

Position equation of a particle is given by

• x = t² + 2t + 2

To Find :

Average velocity of particle between 0s and 2s.

Solution :

❖ In order to find velocity of the particle we have to differentiate the given position equation with respect to time.

$\dag\:\underline{\boxed{\bf{\orange{v=\lim\limits_{t\to 0}^{}\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}}$

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

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

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

$\bf:\implies\:v=2t+2$

A] Velocity at t = 0s :

$\sf:\implies\:v_0=2(0)+2$

$\sf:\implies\:v_0=0+2$

$\bf:\implies\:v_0=2\:ms^{-1}$

B] Velocity at t = 2s :

$\sf:\implies\:v_2=2(2)+2$

$\sf:\implies\:v_2=4+2$

$\bf:\implies\:v_2=6\:ms^{-1}$

C] Average velocity of particle :

$\sf:\implies\:v=\dfrac{v_0+v_2}{2}$

$\sf:\implies\:v=\dfrac{2+6}{2}$

$\sf:\implies\:v=\dfrac{8}{2}$

$:\implies\:\underline{\boxed{\bf{\purple{v=4\:ms^{-1}}}}}$

Answer 2

Question :

Given the position of a particle as x = t² + 2t + 2 m, the average velocity between 0s and 2s is

A) 10 m/s

B) 4 m/s

C) 8 m/s

D) 6 m/s

Given :

Position equation of a particle is given by

x = t² + 2t + 2

To Find :

Average velocity of particle between 0s and 2s.

Solution :

❖ In order to find velocity of the particle we have to differentiate the given position equation with respect to time.

$\dag\:\underline{\boxed{\bf{\orange{v=\lim\limits_{t\to 0}^{}\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}}$

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

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

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

$\bf:\implies\:v=2t+2$

A] Velocity at t = 0s :

$\sf:\implies\:v_0=2(0)+2$

$\sf:\implies\:v_0=0+2$

$\bf:\implies\:v_0=2\:ms^{-1}$

B] Velocity at t = 2s :

$\sf:\implies\:v_2=2(2)+2$

$\sf:\implies\:v_2=4+2$

$\bf:\implies\:v_2=6\:ms^{-1}$

C] Average velocity of particle :

$\sf:\implies\:v=\dfrac{v_0+v_2}{2}$

$\sf:\implies\:v=\dfrac{2+6}{2}$

$\sf:\implies\:v=\dfrac{8}{2}$

$:\implies\:\underline{\boxed{\bf{\purple{v=4\:ms^{-1}}}}}$