Question

The motion of an avalanche is described by s1t2 􏰀 3t2, where s is the distance, in metres, travelled by the leading edge of the snow at t seconds.
a. Find the distance travelled from 0s to 5s.
b. Find the rate at which the avalanche is moving from 0s to10s.
c. Find the rate at which the avalanche is moving at 10s.
d. How long, to the nearest second, does the leading edge of the snow take to move 600 m?

Answer 1

the motion of the avaknce is described by s(t)=3t^2

Answer 2

when t = 0, s = 0
when t = 5 , s = 3(25) = 75

b) when t = 10 , s = 300
rate = (300-0)/(10-0) = 30 m/s

c) v(t) = 6t
when t = 10, v(10) = 60 m/s

d) 3t^2 = 600
t^2 = 200
t = √200 = appr 14.1 seconds

Answer 3

The next three terms

Answer 4

a) s(0) =0
s(5) = 3t^2 = 3(5)^2 = 75m

b) s(10) = 3(10)^2 = 300
s(10) - s(0) / 10-0 = 30m/s

c)s(10) = 300 s(10+h) = 3(10+h)^2 = 300+60h+3h^2

s(10 +h) - s(10) / h
= 60 + 3h ; where limit h->0
=60m/s

d)600=3t^2
200 = t^2
t = 14.1 s