A leaky 10-kg bucket is lifted from the ground to a height of 14 m at a constant speed with a rope that weighs 0.7 kg/m. Initially the bucket contains 42 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14-m level. Find the work done. (Use 9.8 m/s? for g.)
Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter x" as x.)
im
E
AX
Express the work as an integral.
Evaluate the integral. (Round your answer to the nearest Integer.)
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Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".