1) An exit ramp takes cars from a highway to a road. To estimate the ramps lengt

Question

1) An exit ramp takes cars from a highway to a road. To estimate the ramps length, the engineer calculates the distance covered by a deaccerelerating car, going from 110 ft/sec (about 75mph) to 44 ft/sec, at a constant deacceleration of 6 ft/sec^2. That is, the speed descends linearly over 11 secs. Find the distance covered.

You can solve this with simple integration techniques.

2) Let f(x) be a continuous function defined on an interval I . Suppose that F(x) is an antiderivative for f(x).

a) Let C be a number. True/False: The function F(x)+C is also an antiderivative of f(x).

b) Let C be a number. True/False: The function F(x)+Cx is an antiderivative of f(x)+Cx.

c) True/False: If G(x) is another antiderivative of f(x), then there is some number Csuch that G(x)=F(x)+C.

Explanation / Answer

1.Since the deceleration is constant, we have s = (v2 - u2)/2a = (442 - 1102)/(-2x6) = 847 ft

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