GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
75 views
A rail engine accelerates from its stationary position for 8 seconds and travels a distance of 280m. According to the Mean Value Theorem, the speedometer at a certain time during acceleration must read exactly.

(A) 0km/h

(B) 8km

(C) 75km/h

(D) 126km/h
asked in Calculus by Active (1.5k points)   | 75 views

1 Answer

+6 votes
Best answer

We know according to Lagrange's Mean Value Theorem , we have :

If a function is continuous in [a,b] and differentiable in (a , b) then there is a point x s.t :

f'(x)  =  [f(b) - f(a)] / [ b - a ]

So considering f'(x) as velocity here and f(x) as displacement here and time as x here , so we have :

Velocity at one point in the entire time interval = Slope

                                                                    = ( 280 - 0 ) / 8

                                                                    = 35 m/s

                                                                    = 35 * 18 / 5

                                                                    = 126 km / hr

Hence D) is the correct answer according to Lagrange's Mean Value Theorem..

answered by Veteran (60.3k points)  
selected by
Top Users Jan 2017
  1. Debashish Deka

    9872 Points

  2. sudsho

    5596 Points

  3. Habibkhan

    5498 Points

  4. Bikram

    5350 Points

  5. Vijay Thakur

    4508 Points

  6. Arjun

    4458 Points

  7. Sushant Gokhale

    4410 Points

  8. saurabh rai

    4236 Points

  9. santhoshdevulapally

    3906 Points

  10. Kapil

    3892 Points

Monthly Topper: Rs. 500 gift card

19,481 questions
24,261 answers
54,211 comments
20,405 users