For the following exercises, use the fact that a falling body with friction equal to velocity squared obeys the equation d v / d t = g − v 2 . 420. Derive the previous expression for v ( t ) by integrating d v g − v 2 = d t .
For the following exercises, use the fact that a falling body with friction equal to velocity squared obeys the equation d v / d t = g − v 2 . 420. Derive the previous expression for v ( t ) by integrating d v g − v 2 = d t .
For the following exercises, use the fact that a falling body with friction equal to velocity squared obeys the equation
d
v
/
d
t
=
g
−
v
2
.
420. Derive the previous expression for
v
(
t
)
by integrating
d
v
g
−
v
2
=
d
t
.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
A spring is stretched a distance x from its original length.
The potential energy stored in the spring is directly proportional to x squared.
The potential energy stored in the spring when it is stretched 0.25m is 600 J.
Derive an equation for the potential energy stored in the spring.
Note: You must determine the value of the constant.
A particle starts to move at Q and travels in a straight line with velocity v cms-1, where v = 2t-t2 and t is the time in seconds after leaving Q. The particle comes to rest at A.
Calculate:
a. the value of t at A.
b. the acceleration, a cms-2
c. the distance, s cm, from Q to A.
d. the total distance covered from t=o to t=4.
A researcher is nuning a simulation of an upward rocket to study the upward velocity of the
rocket using various fuel consumption rates. The researcher has found that the upward velocity
of the rocket can be represented by the following equation,
mo
v = u In
gt
Amo-qt.
where v=upward velocity of the rocket (m/s), u= the velocity at which fuel is expelled relative
to the rocket (m/s), m, = the initial mass of the rocket (kg), q = the fuel consumption rate
(kg/s), g = the downward accelemation of gravity (m/s), and t = time taken by the rocket for
the whole motion (s). If u = 1,500 m/s, m, = 125,000 kg, q = 2,300 kg/s and g= 9.81 m/s are
the values used by the researcher in one of his simulations, estimate the time, t at which v =
680 m/s using False Position method. It is known that the time, t is somewhere between 15 s
and 35 s. Perform THREE (3) iterations only and calculate the approximate percent relative
error, Ea| for every iteration.
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