V = t^2 - 9t + 18
position, s
s = t^3 /3 - 4.5t^2 +18t + C
t = 0, s = 1 => 1=C => s = t^3/3 -4.5t^2 + 18t + 1
Average velocity: distance / time
distance: t = 8 => s = 8^3 / 3 - 4.5 (8)^2 + 18(8) + 1 = 27.67 m
Average velocity = 27.67 / 8 = 3.46 m/s
t = 5 s
v = t^2 - 9t + 18 = 5^2 - 9(5) + 18 = -2 m/s
speed = |-2| m/s = 2 m/s
Moving right
V > 0 => t^2 - 9t + 18 > 0
(t - 6)(t - 3) > 0
=> t > 6 and t > 3 => t > 6 s => Interval (6,8)
=> t < 6 and t <3 => t <3 s => interval (0,3)
Going faster and slowing dowm
acceleration, a = v' = 2t - 9
a > 0 => 2t - 9 > 0 => 2t > 9 => t > 4.5 s
Then, going faster in the interval (4.5 , 8) and slowing down in (0, 4.5)
<span>Scientific theories are tested and proven over time; they are then considered scientific laws.
Sometimes however, they are proven wrong, and so they do not become laws
hope this helps</span>
Diceplacement is the distance an object has traveled in a certain direction
for example, if you were to walk North for 20m, then east for 40m, the <u>distance</u> you have traveled is 60m however your displacement is the distance between your starting position and your end position;
sqrt(20^2+40^2) = 44.7m
and because displacement is a vector, there needs to be a direction;
sin(theta)=40/44.7
theta=63.4 degrees East of North
therefore the true displacement is 44.7m at 63.4 degrees East of North
KE=1/2 mv²
= 1/2 × 70 × (6)²
= 1260
F=ma
Tension - weight = mass x acceleration
T - 5(9.81) = 5 x 1
T = 5 + 5(9.81)
T = 54.05 N
T ≈ 54 N
