Ask a Doubt

Request a call back

Join NOW to get access to exclusive study material for best results

Home
JEE-Main
Ask a Doubt
View Answer

JEE Class main Answered

A vehicle travels from city A to city B. During the first part of the journey its average speed is whilst in the rest of the journey it is. By what factor is the length of the second part of the journey longer than that of the first part if the average speed calculated for

question image

Asked by satyamsinghtech367 | 04 Jul, 2022, 09:06: PM

Expert Answer

Part (a)

Speed = aritmatic mean of speed of both parts of journey = ( v₁ + v₂ ) /2

Let S₁ be the distance travelled in first part and S₂ be the distance travelled in second part.

We can write the following expression for total time of journey

begin mathsize 14px style S subscript 1 over v subscript 1 plus S subscript 2 over v subscript 2 space equals fraction numerator S subscript 1 plus S subscript 2 over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis divided by 2 end fraction end style

begin mathsize 14px style S subscript 1 over v subscript 1 minus fraction numerator 2 S subscript 1 over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction space equals space fraction numerator 2 S subscript 2 over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction minus S subscript 2 over v subscript 2 end style

begin mathsize 14px style S subscript 1 space open parentheses 1 over v subscript 1 minus fraction numerator 2 over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction close parentheses space equals space S subscript 2 open parentheses fraction numerator 2 over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction minus 1 over v subscript 2 close parentheses end style

begin mathsize 14px style S subscript 1 over v subscript 1 space cross times fraction numerator stretchy left parenthesis v subscript 2 minus v subscript 1 stretchy right parenthesis over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction space equals space S subscript 2 over v subscript 2 space cross times fraction numerator stretchy left parenthesis v subscript 2 minus v subscript 1 stretchy right parenthesis over denominator left parenthesis v subscript 1 plus v subscript 2 right parenthesis end fraction end style

begin mathsize 14px style S subscript 2 over S subscript 1 space equals space v subscript 2 over v subscript 1 end style

--------------------------------------------------------------------------

Part (b)

Speed = geometric mean of speed of both parts of journey =

begin mathsize 14px style square root of v subscript 1 v subscript 2 end root end style

Let S₁ be the distance travelled in first part and S₂ be the distance travelled in second part.

We can write the following expression for total time of journey

begin mathsize 14px style S subscript 1 over v subscript 1 plus S subscript 2 over v subscript 2 space equals fraction numerator S subscript 1 plus S subscript 2 over denominator square root of v subscript 1 v subscript 2 end root end fraction end style

begin mathsize 14px style fraction numerator S subscript 1 v subscript 2 space plus space S subscript 2 v subscript 1 over denominator v subscript 1 v subscript 2 end fraction space equals fraction numerator S subscript 1 plus S subscript 2 over denominator square root of v subscript 1 v subscript 2 end root end fraction end style

begin mathsize 14px style fraction numerator S subscript 1 v subscript 2 space plus space S subscript 2 v subscript 1 over denominator square root of v subscript 1 v subscript 2 end root end fraction space equals left parenthesis space S subscript 1 plus S subscript 2 space right parenthesis space end style

begin mathsize 14px style S subscript 1 v subscript 2 minus space S subscript 1 square root of v subscript 1 v subscript 2 end root space equals space S subscript 2 space square root of v subscript 1 v subscript 2 end root space minus space S subscript 2 space v subscript 1 end style

begin mathsize 14px style S subscript 1 square root of v subscript 2 end root space open parentheses square root of v subscript 2 end root space minus space square root of v subscript 1 end root close parentheses space equals space S subscript 2 square root of v subscript 1 end root space open parentheses square root of v subscript 2 end root space minus space square root of v subscript 1 end root close parentheses space end style

begin mathsize 14px style S subscript 2 over S subscript 1 space equals space square root of v subscript 2 over v subscript 1 end root end style

---------------------------------------------------------

Part (c)

Speed = harmonic mean of speed of both parts of journey =

begin mathsize 14px style fraction numerator 2 space v subscript 1 v subscript 2 over denominator v subscript 1 plus space v subscript 2 end fraction end style

Let S₁ be the distance travelled in first part and S₂ be the distance travelled in second part.

We can write the following expression for total time of journey

begin mathsize 14px style S subscript 1 over v subscript 1 plus S subscript 2 over v subscript 2 space equals open parentheses S subscript 1 plus S subscript 2 close parentheses fraction numerator open parentheses v subscript 1 plus v subscript 2 close parentheses over denominator 2 v subscript 1 v subscript 2 end fraction end style

begin mathsize 14px style fraction numerator S subscript 1 v subscript 2 plus S subscript 2 v subscript 1 over denominator v subscript 1 v subscript 2 end fraction space equals open parentheses S subscript 1 plus S subscript 2 close parentheses fraction numerator open parentheses v subscript 1 plus v subscript 2 close parentheses over denominator 2 v subscript 1 v subscript 2 end fraction end style

begin mathsize 14px style 2 open parentheses S subscript 1 v subscript 2 space plus space S subscript 2 v subscript 1 close parentheses space equals space open parentheses S subscript 1 plus S subscript 2 close parentheses open parentheses v subscript 1 plus v subscript 2 close parentheses end style

begin mathsize 14px style open parentheses S subscript 1 v subscript 2 space plus space S subscript 2 v subscript 1 close parentheses space equals space stretchy left parenthesis S subscript 1 v subscript 1 space plus space S subscript 2 v subscript 2 stretchy right parenthesis end style

begin mathsize 14px style S subscript 1 open parentheses v subscript 2 space minus space v subscript 1 close parentheses space equals space S subscript 2 stretchy left parenthesis v subscript 2 space minus space v subscript 1 stretchy right parenthesis end style

begin mathsize 14px style S subscript 2 over S subscript 1 space equals space 1 end style

-------------------------------------------------------------------------

Part (d)

Speed = weighted arithmatic mean of speed of both parts of journey =

begin mathsize 14px style fraction numerator v subscript 1 plus space k space v subscript 2 over denominator 1 plus space k end fraction end style

Let S₁ be the distance travelled in first part and S₂ be the distance travelled in second part.

We can write the following expression for total time of journey

begin mathsize 14px style S subscript 1 over v subscript 1 plus S subscript 2 over v subscript 2 space equals open parentheses S subscript 1 plus S subscript 2 close parentheses fraction numerator open parentheses 1 space plus k close parentheses over denominator stretchy left parenthesis v subscript 1 plus k space v subscript 2 stretchy right parenthesis end fraction end style

begin mathsize 14px style S subscript 1 open square brackets 1 over v subscript 1 space minus space fraction numerator 1 plus k over denominator v subscript 1 plus k v subscript 2 end fraction close square brackets space equals space S subscript 2 space open square brackets fraction numerator 1 plus k over denominator v subscript 1 plus k v subscript 2 end fraction space minus space 1 over v subscript 2 space close square brackets end style

begin mathsize 14px style S subscript 1 space open square brackets fraction numerator k left parenthesis v subscript 2 minus v subscript 1 right parenthesis over denominator v subscript 1 stretchy left parenthesis v subscript 1 plus k space v subscript 2 stretchy right parenthesis end fraction close square brackets space equals space S subscript 2 space open square brackets fraction numerator left parenthesis v subscript 2 minus v subscript 1 right parenthesis over denominator v subscript 2 stretchy left parenthesis v subscript 1 plus k space v subscript 2 stretchy right parenthesis end fraction space close square brackets end style

begin mathsize 14px style S subscript 2 over S subscript 1 space equals space k space cross times v subscript 2 over v subscript 1 end style

---------------------------------------------------------------------

Answered by Thiyagarajan K | 05 Jul, 2022, 08:28: AM

Practice Test

Answered Unanswered My Questions My Answers

JEE main - Physics

how to draw straight line graph and how to identify y-intercept and slope

Asked by Machinenineha | 27 Mar, 2024, 05:28: PM

ANSWERED BY EXPERT

JEE main - Physics

s

question image

Asked by baskaranfathima83 | 21 Jan, 2024, 09:34: PM

ANSWERED BY EXPERT

JEE main - Physics

a body covers 1/3 part of its journey with a velocity of 2 m/s , next 1/3 part with a velocity of 3m/s and rest journey with a velocity 6m/s .The average velocity of the body will be

question image

Asked by tripathiji9876good | 10 Jan, 2024, 04:22: PM

ANSWERED BY EXPERT

JEE main - Physics

if the leniar momentum is increased by 5%then the kinetic energy will be increased by

Asked by meenu0000156 | 05 Jan, 2024, 12:05: PM

ANSWERED BY EXPERT

JEE main - Physics

answer

question image

Asked by myselfsnehu5577 | 29 Nov, 2023, 01:19: PM

ANSWERED BY EXPERT

JEE main - Physics

a boat moves with velocity which is n times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting. I din understand how dx/d theta=ud/v sec theta tan theta-d sec^2 theta like whr did the addition sec theta come from??? so pls explain tht

Asked by joanmaria916 | 17 Jul, 2023, 11:24: AM

ANSWERED BY EXPERT

JEE main - Physics

As shown in Figure, a bullet weighs 0.3 N and moving with a velocity of 400 m/sec hits centrally a 30 N block of wood moving away at 15 m/sec and gets embedded in it. Find the velocity of the bullet after the impact and the amount of kinetic energy lost.

question image

Asked by theavengers0203 | 22 May, 2023, 11:54: PM

ANSWERED BY EXPERT

JEE main - Physics

physics questions

question image

Asked by mc8may | 03 Apr, 2023, 03:41: PM

ANSWERED BY EXPERT

JEE main - Physics

An object moves from y = 12 m to y = 15 m in 5 s. What can be said about the magnitude of displacement and the path length?

Asked by khushpatel9579 | 16 Feb, 2023, 07:50: PM

ANSWERED BY EXPERT

JEE main - Physics

A particle start from rest and move along a straight line with uniform acceleration the ratio of time to cover successive distance in the ratio 1:3 is

Asked by yadavashishkryadav | 13 Jan, 2023, 08:38: AM

ANSWERED BY EXPERT

My Class Videos Tests Plans Ask a Doubt

Get Latest Study Material for Academic year 24-25 Click here

×