we know that center of mass is given as
r = (m₁ 
+ m₂ 
)/(m₁ + m₂)
taking derivative both side relative to "t"
dr/dt = (m₁ d/dt + m₂ d/dt)/(m₁ + m₂)
v = (m₁ 
+ m₂ 
)/(m₁ + m₂)
taking derivative again relative to "t" both side
dv/dt = (m₁ d/dt + m₂ d/dt)/(m₁ + m₂)
a= (m₁ 
+ m₂ 
)/(m₁ + m₂)
"Acceleration" does NOT mean speeding up. It also doesn't mean
slowing down. Acceleration means ANY change in the speed
OR DIRECTION of motion.
The only kind of motion that's NOT accelerated is motion at a steady
speed AND in a straight line.
Even when your speed is steady, you're accelerating if your direction
is changing.
A few examples:
(no speeds are changing):
-- driving on a curved road, or turning a corner
-- going around a curve on a skateboard, a bike, or a Segway
-- running on a quarter-mile track
-- an Indy car cruising a practice lap around the track
-- water spinning, getting ready to go down the drain
-- any point on the blade of a fan
-- the little ball going around the inside of a Roulette wheel
-- the Moon in its orbit around the Earth
-- the Earth in its orbit around the sun
When the object is at the top of the hill it has the most potential energy. If it is sitting still, it has no kinetic energy. As the object begins to roll down the hill, it loses potential energy, but gains kinetic energy. The potential energy of the position of the object at the top of the hill is getting converted into kinetic energy. Hope this helped. :)
Answer:
a = 0.7267
, acceleration is positive therefore the speed is increasing
Explanation:
The definition of acceleration is
a = dv / dt
they give us the function of speed
v = - (t-1) sin (t² / 2)
a = - sin (t²/2) - (t-1) cos (t²/2) 2t / 2
a = - sin (t²/2) - t (t-1) cos (t²/2)
the acceleration for t = 4 s
a = - sin (4²/2) - 4 (4-1) cos (4²/2)
a = -sin 8 - 12 cos 8
remember that the angles are in radians
a = 0.7267
the problem does not indicate the units, but to be correct they must be m/s²
We see that the acceleration is positive therefore the speed is increasing
that is an example of negative acceleration because it is slowing down
