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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 Loyal (4.9k points) 4 44 88 | 201 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 (89.4k points) 15 58 296
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