#1 and #2 look ok (except that x(3) = 18 units, not units/s)
#3 flea moving right when x'(t) > 0 (s increasing)
#4 evaluate x(t) at the extrema from part 2.
Check with this graph:
http://www.wolframalpha.com/input/?i=t^3+-+9t^2+%2B+24t
#5 x(5)-x(0)
#6 ∫[0,5] (1+(x')^2) dt
= ∫[0,5] √(1+(3t^2-18t+24)^2) dt
= 29 units
Not sure where the 12 came from.
A flea moves along the line y = -3 according to the equation: x = t^3 - 9t^2 + 24t where x is its x coordinate at time t secs.
Determine:
1) the position, velocity, and acceleration of the flea at time 3 secs.
Answer: position - 3^3 - 9(3)^2 + 24(3) = 18 units/second
velocity - 3(3)^2 - 18(3) + 24 = -3 units/second
acceleration: 6(3) - 18 = 0 units/second^2
2) the time(s) when the flea is at rest
Answer: 3t^2 - 18t + 24 = 0
3(t^2 - 6t + 8) = 0
3(t-4)(t-2) = 0
t = 4 secs or t = 2 secs
3) the interval(s) when the flea is moving right and the interval(s) when he is moving left
4) the leftmost and rightmost positions of the flea
5) the net displacement of the flea from time 0 sec. to time 5 sec.
6) the total distance traveled by the flea during the 1st 5 seconds
Answer: 12 units
Are my answers correct? I'm not sure how to find the answers to the other ones.
1 answer