Q1) Q2) Ice is forming on a pond at a rate given by dy/dt = k t where y is the t

Question

Q1)

Q2)

Ice is forming on a pond at a rate given by dy/dt = k t where y is the thickness of the ice in inches at time t measured in house since the ice started forming, and k is a positive constant. Find y as a function of t. Assume there is no ice initially. y(t) = A car going 60 ft/sec brakes to a stop in five seconds. Assume the deceleration is constant. Graph the velocity against time t for 0 t 5 seconds . Then represent, as an area, the total distance traveled from the time the brakes are applied until the car comes to a stop. Find the total distance traveled. ft

Explanation / Answer

1.) dy / dt = k sqrt t

We can write as

dy = k sqrt t dt

On integrating,

y = k t^3/2 / (3/2) + c

y = 2kt^(3/2)/3 + c

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