Question

1. A car travels with speed 3 m s-1 for the first half
distance of the journey and with speed 6 ms for
the remaining half. What is the average
speed of
the entire journey?
[NCERT Pg. 42]
(1) 6 ms-
(2) 18 m s-1
(3) 9 m s-1
(4) 4 m s-1​

Answer 1

Answer

• Avg Speed is 4 m/s {Option D}

Explanation

Given

• A car travels first half of a journey with 3 m/s & another half with a speed of 6 m/s

To Find

• Average Speed of the body?

Solution

Assume that

• Distance travelled by the car in both cases = x m
• Total distance travelled = 2x m

✭ First Half of the journey

→ Speed = Distance/Time

→ Time = Distance/Speed

→ Time (first half) = x/3

✭ Second half of the journey

→ Speed = Distance/Time

→ Time = Distance/Speed

→ Time (second half) = x/6

✭ Average Speed of the body

→ Avg speed = Total distance/Total time

→ Avg speed = 2x/[x/3 + x/6]

→ Avg speed = 2x/[(6x + 3x)/18]

→ Avg speed = 2x × 18/9x

→ Avg speed = 4 m/s

Answer 2

Answer:

${\underline {\sf {\underline{☃Given:}}}}$

• Car travels for first half of journey with speed = 3m/s
• Car travels for second half of journey with speed = 6m/s

$\underline{ \sf{ \underline{ ☃Find:}}}$

• Average speed of entire journey

$\underline{ \sf{ \underline{ ☃Solution:}}}$

We know that ⤵

${ \boxed{ \sf{Average \: Speed = \frac{Total \: Distance}{ Total \: Time} }}}$

So, let's find the total distance and total time

☯Total Distance:-

Let take the distance travelled by cars as x

So, Total distance travelled by both cars = 2x

☯Total time:-

☘Time of first half of journey :-

From the formula⤵

${ \boxed{ \sf{Time = \frac{Distance}{Speed} }}}$

${ \sf{ \to{Time \: of \: first \: half= \frac{x}{3} }}}$

☘Time of Second half of journey:-

From the formula ⤵

${ \boxed{ \sf{Time = \frac{Distance}{Speed} }}}$

${ \sf{ \to{Time \: of \: second\: half= \frac{x}{6} }}}$

☞Average speed of body:-

${ \to{ \sf{Average \: Speed = \frac{2x}{ \frac{x}{3} + \frac{x}{6} } }}}$

${ \to{ \sf{Average \: Speed = \frac{2x}{ \frac{6x + 3x}{18} } }}}$

${ \to{ \sf{Average \: Speed = \frac{2x}{ \frac{9x}{18} } }}}$

${ \to{ \sf{Average \: Speed = 2x \times \frac{18}{9 x } }}}$

${ \to{ \sf{Average \: Speed = \frac{36x}{9x} }}}$

${ \to{ \sf{Average \: Speed = 4}}}$

Therefore,

Average speed of the body is 4m/s