it is just a matter of integration and using initial conditions since in general dv/dt = a it implies v = integral a dt
v(t)_x = integral a_{x}(t) dt = alpha t^3/3 + c the integration constant c can be found out since we know v(t)_x at t =0 is v_{0x} so substitute this in the equation to get v(t)_x = alpha t^3 / 3 + v_{0x}
similarly v(t)_y = integral a_{y}(t) dt = integral beta - gamma t dt = beta t - gamma t^2 / 2 + c this constant c use at t = 0 v(t)_y = v_{0y} v(t)_y = beta t - gamma t^2 / 2 + v_{0y}
so the velocity vector as a function of time vec{v}(t) in terms of components as[ alpha t^3 / 3 + v_{0x} , beta t - gamma t^2 / 2 + v_{0y} ]
similarly you should integrate to find position vector since dr/dt = v r = integral of v dt
r(t)_x = alpha t^4 / 12 + + v_{0x}t + c let us assume the initial position vector is at origin so x and y initial position vector is zero and hence c = 0 in both cases
r(t)_y = beta t^2/2 - gamma t^3/6 + v_{0y} t + c here c = 0 since it is at 0 when t = 0 we assume
r(t)_vec = [ r(t)_x , r(t)_y ] = [ alpha t^4 / 12 + + v_{0x}t , beta t^2/2 - gamma t^3/6 + v_{0y} t ]
Displacement is d
Vf² = Vi² + 2 g d
(-20²) = (+10²) + 2 (-9.8) d
-19.6 d = 300
d = -15.3 m
negative means lower
time is t
d = Vi t + 1/2 g t²
-15.3 = 10 t + (-4.9) t²
4.9 t² - 10 t -15.3 = 0
t = 3.06 s
Hope this helps -John
Explanation:
The new volume of water = 25 ml
The old volume of water = 15 ml
The difference = 25 - 15 but what are the units?
Since the question asks for force, the units must start out as 10 mL
In water 1 mL has a mass of 1 gram, so the answer is 10 grams.
Grams are units of mass, not weight. You should convert this into newtons.
10 grams = 1/1000 = 0.01 kg
1 kg has a weight of 9.81 Newtons
0.01 kg has a weight 0.081 Newtons
If you have never seen a Newton before, then the answer is 10 grams
Unicellular: An organism that consists of a single cell
Multicellular: An organism with multiple cells
Eukaryotic: A cell that contains a nucleus
Prokaryotic: A cell with no nucleus
Autotrophic: An organism that has the ability to make their own food
Heterotrophic: Organism that cannot create their own food
Asexual reproduction: When an organism has the ability to create offspring without the help of another organism
Sexual Reproduction: When two organisms create an offspring using the gametes
<span>fluid friction of the air also known as drag</span>
