Question

if a body moves with velocity v and 3v for equal interval of time t then its average velocity is​

Answer 1

Given :

A body moves with velocity v and 3v for equal interval of time t.

To Find :

Average velocity of body.

Solution :

❖ Average speed is defined as the ratio of total distance travelled to the total time taken.

• It is a scalar quantity having only magnitude.
• It can't be negative or zero.
• SI unit : m/s
• Dimension formula : [L¹T‾¹]

$\sf:\implies\:v_{av}=\dfrac{d_1+d_2}{t_1+t_2}$

$\sf\:We\:know\:that,\:Distance=Velocity\times Time$

$\sf:\implies\:v_{av}=\dfrac{v_1t_1+v_2t_2}{t_1+t_2}$

$\sf:\implies\:v_{av}=\dfrac{vt+3vt}{t+t}$

$\sf:\implies\:v_{av}=\dfrac{4vt}{2t}$

$\sf:\implies\:v_{av}=\dfrac{4v}{2}$

$:\implies\:\underline{\boxed{\bf{\orange{v_{av}=2v}}}}$

Answer 2

Given :

A body moves with velocity v and 3v for equal interval of time t.

To Find :

Average velocity of body.

Solution :

❖ Average speed is defined as the ratio of total distance travelled to the total time taken.

It is a scalar quantity having only magnitude.

It can't be negative or zero.

SI unit : m/s

Dimension formula : [L¹T‾¹]

$\sf:\implies\:v_{av}=\dfrac{d_1+d_2}{t_1+t_2}$

$\sf\:We\:know\:that,\:Distance=Velocity\times Time$

$\sf:\implies\:v_{av}=\dfrac{v_1t_1+v_2t_2}{t_1+t_2}$

$\sf:\implies\:v_{av}=\dfrac{vt+3vt}{t+t}$

$\sf:\implies\:v_{av}=\dfrac{4vt}{2t}$

$\sf:\implies\:v_{av}=\dfrac{4v}{2}$

$:\implies\:\underline{\boxed{\bf{\orange{v_{av}=2v}}}}$