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Wize University Calculus 1 Textbook > Applications of Integration for Physical Science

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Suppose a car hits the brakes at full power and comes to a complete stop after 50 meters. Assuming that the deceleration caused by the brakes is a constant −10 m/sec2-10 \text{ m/sec}^2, find the speed of the car (in meters per second, to two decimal places) when it began braking.
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How much work is required to empty a conical tank of height 3m, (upper) radius 1m, of a liquid of density ρ\rho by pumping the liquid 1.5 meters above the top of the tank?

A triangular moat is dug around a point. If the x-axis represents the ground, the triangle is bounded by points (0,2), (3,2), (1,0)(0,2), \, (3,2), \, (1,0), and the axis of rotation is x=4x=4.
(a) How much water is required to fill the moat? (Provide an exact answer only.)
(b) How much work is required to empty the moat, if the pump empties three metres above the ground? (The density of water is 1.) (Leave your answer in terms of π,g\pi, g.)
A metal shop is producing thin pieces of metal as part of a larger set of furniture. The thin piece of metal is 1212 cm long, with mass density per unit length ρ(x)=11+x\rho(x) = \frac{1}{1 + x} grams per cm from one end to the other.

a) Find the total mass of the piece.

b) Find the center of mass of the piece.
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Consider a dam that has the shape of an upside down isosceles triangle, with base 50m50m and height 40m40 m . Find the force on the dam due to hydrostatic pressure when the water level is 30m30m high.