1.Suppose that a car’s speedometer reads 15 mi/h at 2:00PM. and 35 mi/h at 2:20P
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1.Suppose that a car’s speedometer reads 15 mi/h at 2:00PM. and 35 mi/h at 2:20PM. Assuming the car’s speed is a differentiable function of time show using the MVT that at some instant in this time interval the car’s acceleration was 60 mi/h2. 1.Suppose that a car’s speedometer reads 15 mi/h at 2:00PM. and 35 mi/h at 2:20PM. Assuming the car’s speed is a differentiable function of time show using the MVT that at some instant in this time interval the car’s acceleration was 60 mi/h2. 1.Suppose that a car’s speedometer reads 15 mi/h at 2:00PM. and 35 mi/h at 2:20PM. Assuming the car’s speed is a differentiable function of time show using the MVT that at some instant in this time interval the car’s acceleration was 60 mi/h2.Explanation / Answer
Mean value theorem is 1. if f is continuous fn in the closed interval [a,b]
2. f is differentiable in the open interval (a,b) then
there exist atleast ' 1' value c such that f ' ( c) = [ f(b) - f(a) ] / ( b - a )
f( 2 ) = 15 , , f ( 7/3 ) == 35 and a= 2 and b = 7/3 . substituing in the above formula
f ' ( c ) = (35 - 15) / 1/3 = 20 x 3 = 60 and f ' ( c ) is the rate of velocity hence it is the cceleration at the point c in the iopen interval (2 , 7/3)
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