Question

2. A person travels along a straight road for half the distance with velocity v, and the remaining half
distance with velocity v, the average velocity is given by
V2
V q + V₂
21, V2
2)
3)
V₂ + V₂
2
1) v, V2
2​

Answer 1

Given :

▪ A person travels first half of the total distance at a velocity of $\sf{V_1}$ and second half of the total distance at a velocity of $\sf{V_2}$.

To Find :

▪ Average velocity of person.

Concept :

✴ Average velocity is defined as the ratio of total distance travelled to the time taken.

✴ It is a vector quantity.

✴ It has both magnitude as well as direction.

✴ It can be positive, negative or zero.

✴ SI unit : m/s

Calculation :

↗ Let body covers first half (d/2) of the total distance in time $\sf{t_1}$ at a velocity of $\sf{V_1}$ and second half (d/2) of the total distance in time $\sf{t_2}$ at a velocity of $\sf{V_2}$, then average velocity of body is given by

$\dashrightarrow\tt\:V_{av}=\dfrac{d_1+d_2}{t_1+t_2}\\ \\ \dashrightarrow\tt\:V_{av}=\dfrac{\frac{d}{2}+\frac{d}{2}}{t_1+t_2}\\ \\ \green{\circ}\sf\:{\huge{[}}\red{time=\dfrac{distance}{velocity}}{\huge{]}}\\ \\ \dashrightarrow\tt\:V_{av}=\dfrac{d}{\frac{d}{2V_1}+\frac{d}{2V_2}}\\ \\ \dashrightarrow\tt\:V_{av}=\dfrac{2}{\frac{V_1+V_2}{V_1V_2}}\\ \\ \dashrightarrow\underline{\boxed{\bf{\purple{V_{av}=\dfrac{2V_1V_2}{V_1+V_2}}}}}\:\orange{\bigstar}$

Answer 2

GiVen:-

A person travels with the half distance at a velocity of $\sf{V_{1}}$ and the second half distance at a velocity of $\sf{V_{2}}$

To Find:-

Average velocity of person.

Concept:-

● It is a vector quantity.

● It has both magnitude and direction.

● It can be negative, positive or zero.

● S. I unit is m/s.

Solution:-

Let the body covers the half(d/2) of the total distance $\sf{t_{1}}$ at a velocity of $\sf{V_{1}}$and second half (d/2) of the distance $\sf{t_{2}}$at a velocity of $\sf{V_{2}}$, then the average velocity of body is given by,

$\mapsto$ Vav $\longrightarrow$ d1+d2/t1+t2

$\longrightarrow {\boxed{\tt{\red{\: Time= \frac{distance}{velocity}}}}}$

$\longrightarrow$ $\sf{V_{av}}$ = 2V1 2v2/V1+V2