# Power Rules of Derivatives

• Nov 18th 2010, 12:00 PM
Power Rules of Derivatives

The motion of an avalanche is described by s(t) = 3t^2, where s is the distance in metres travlled by the leading edge of the avalanche at t seconds.

a) Find the distance travelled from 0 to 5 s

b) find the rate at which the avalanche is moving from 0 s to 10 s

c) find the rate at which the avalanche is moving at 10 s

d) How long, to the nearest second, does the leading edge of the avalanche take to move 600 m?
• Nov 18th 2010, 03:01 PM
skeeter
Quote:

The motion of an avalanche is described by s(t) = 3t^2, where s is the distance in metres travlled by the leading edge of the avalanche at t seconds.

a) Find the distance travelled from 0 to 5 s

s(5)

b) find the rate at which the avalanche is moving from 0 s to 10 s

v{avg} = [s(10) - s(0)]/(10 - 0)

c) find the rate at which the avalanche is moving at 10 s

v(10) = s'(10)

d) How long, to the nearest second, does the leading edge of the avalanche take to move 600 m?

set s(t) = 600 ... solve for t

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