Question

A body covers half the distance with a speed of 20 ms and the other half with a speed if 30 ms the average velocity of the body during the whole journey

Answer 1

ANSWER:

• Avg velocity = 24 m/s

GIVEN:

• A body covers half the distance with a speed of 20 m/s.

• The other half distance with a speed if 30 m/s.

TO FIND:

• The average velocity

EXPLANATION:

Let the distance travelled by the body be 2S

Avg velocity = (Total distance) ÷ (Total time)

Time = Distance ÷ Velocity

$Avg \ velocity = \dfrac{2S}{\dfrac{S}{20}+\dfrac{S}{30}}$

$Avg \ velocity = \dfrac{2S}{S \left(\dfrac{1}{20}+\dfrac{1}{30} \right)}$

$Avg \ velocity = \dfrac{2}{ \bigg(\dfrac{3 + 2}{60} \bigg)}$

$Avg \ velocity = \dfrac{2 \times 60}{5}$

$Avg \ velocity =2 \times 12$

$Avg \ velocity =24 \: m {s}^{ - 1}$

Answer 2

$\bf \huge \fbox \red {Question : - }$

A body covers half the distance with a speed of 20 ms and the other half with a speed if 30 ms the average velocity of the body during the whole journey

$\bf \huge \underline\red{answer : }$

$\bf \: the \: average \: velocity \: of \: the \: body \: during \: the \: whole \: journey \:is \: 24 \: ms ^{ - 1}$

$\bf\huge\green{solution : - }$

$\bf \: Let \: the \: total \: distance \: be \: 2x$

$\bf \ \: For \: first \: half \: distance :$

$\bf \: Speed \: is \: 20 \: {ms}^{ - 1}$

$\bf \: Thus \: time \: taken \: t_1 \: = \frac{x}{20}$

$\bf \: For \: second \: half \: distance :$

$\bf \: Speed \: is \: {30 \: ms}^{ - 1}$

$\bf \: Thus \: time \: taken \: t_2 = \frac{x}{30}$

$\bf \: Average \: Velocity \: V_a_v_g \: = \frac{2x}{t_1 + t_2}$

$\bf \implies \: V_a_v_g \: = \frac{2x}{ \frac{x}{20} + \frac{x}{30} } = \frac{2 \times 20 \times 30}{20 + 30} = 24 {ms}^{ - 1}$

$\bf \huge \pink{\: the \: average \: velocity \: of \: the \: body \: during \: the \: whole \: journey \:is \: 24 \: ms ^{ - 1} }$