-- We know that the y-component of acceleration is the derivative of the
y-component of velocity.
-- We know that the y-component of velocity is the derivative of the
y-component of position.
-- We're given the y-component of position as a function of time.
So, finding the velocity and acceleration is simply a matter of differentiating
the position function ... twice.
Now, the position function may look big and ugly in the picture. But with the
exception of 't' , everything else in the formula is constants, so we don't even
need any fancy processes of differentiation. The toughest part of this is going
to be trying to write it out, given the text-formatting capabilities of the wonderful
envelope-pushing website we're working on here.
From the picture . . . . . y (t) = (1/2) (a₀ - g) t² - (a₀ / 30t₀⁴ ) t⁶
First derivative . . . y' (t) = (a₀ - g) t - 6 (a₀ / 30t₀⁴ ) t⁵ = (a₀ - g) t - (a₀ / 5t₀⁴ ) t⁵
There's your velocity . . . /\ .
Second derivative . . . y'' (t) = (a₀ - g) - 5 (a₀ / 5t₀⁴ ) t⁴ = (a₀ - g) - (a₀ /t₀⁴ ) t⁴
and there's your acceleration . . . /\ .
That's the one you're supposed to graph.
a₀ is the acceleration due to the model rocket engine thrust
combined with the mass of the model rocket
'g' is the acceleration of gravity ... 9.8 m/s² or 32.2 ft/sec²
t₀ is how long the model rocket engine burns
Pick, or look up, some reasonable figures for a₀ and t₀
and you're in business.
The big name in model rocketry is Estes. Their website will give you
all the real numbers for thrust and burn-time of their engines, if you
want to follow it that far.
Answer:
The answer is B the products of photosynthesis are the reactants of cellular respiration
Here is the answer that completes the statement above. We can study how galaxies evolve because THE FARTHER AWAY WE LOOK, THE FURTHER BACK IN TIME WE SEE. This means that the more we discover more about what's happening in the universe, the more we become curious to know how and when it began. Hope this helps.
Answer:
C. 720 N up
Explanation:
Newton's third law states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A"
In this situation, we can imagine the man to be object A and the bench as object B. The force exerted by the man on the bench is:
720 N, down
So according to Newton's third law, the bench must exert an equal and opposite force on the man. Therefore, the force exerted by the bench must be
720 N, up
Explanation:
It is given that,
Mass of the car, m = 1000 kg
Speed of the car, v = 100 km/h = 27.77 m/s
The coefficient of kinetic friction of the tires, 
Let f is the net force acting on the body due to frictional force, such that,
We know that the acceleration of the car in calculus is given by :
, x is the stopping distance
On solving the above equation, we get, x = 78.69 meters
So, the stopping distance for the car is 78.69 meters. Hence, this is the required solution.
