The block's velocity is determined as 10.03 m/s.
<u>Explanation:</u>
According to work energy theorem, the work done on an object is equal to the change in kinetic energy of the object.
So, work done = Kinetic energy
Thus, the velocity can be determined as
Velocity = 10.03 m/s.
So the block's velocity is determined as 10.03 m/s.
-- 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 slope of the line on a velocity vs. time graph represents acceleration.
Explanation:
~~Acceleration is equal to the ratio between the change in velocity of an object and the time taken:
a=\frac{\Delta v}{\Delta t}a=
Δt
Δv
On a velocity-time graph, this ratio corresponds to the slope of the line. In fact, \Delta vΔv corresponds to the increment in the y-value (the velocity), while \Delta tΔt corresponds to the increment in the x-value (the time), therefore their ratio corresponds to the definition of slope of the line.
Answer:
Running is probably the simplest individual sport for promoting both health-related and skill-related fitness. Fencing is often referred to as "mental chess" because it requires dexterity, endurance, and discipline. Individual sports require the coach to make all of the decisions for the athlete.
Answer:
Explanation: what grade are u in?
