A particle moves in a straight line with velocity t-2 - (1/25) ft/s. Find the net displacement and total distance traveled over the time interval [3,6].

Question

A particle moves in a straight line with velocity t^-2 - (1/25) ft/s. Find the net displacement and total distance traveled over the time interval [3,6].

Displacement: ? ft.

Distance: ? ft.

Answer 1

t^2 - t/25

plug in 3 and 6 and take their difference

(6)^2 - 6/25 = 36 -6/25 = 35 19/25 = 35.76

(3)^2 - 3/25 = 9 -3/25 = 8 22/25 = 8.88

35.76-8.88 = 26.88 feet = net displacement

UNLESS maybe you really wrote

t^-2 - t/25,

=1/t^2 - t/25

1/36 -6/25 = 25/(36)(25) - 36/(36)(25)

= -11/900 = -0.01222...

1/9 - 3/25 = 35/(9)(35) - 9/9(25)

=26/225= .11555...

-11/900 to 26/225 = -11(225)/900(225) + 26(900)/900(225)

= (23,400-2,475)/202,500

= 2025/202500 = 0.096774193 = net displacement