Answer:
Explanation:
The acceleration of the bycicle is given by:
where
v = 20 m/s is the final velocity of the bike
u = 40 m/s is the initial velocity
t = 5 s is the time interval
Substituting numbers, we find
and the acceleration is negative, which means that the bycicle is slowing down.
The jigsaw can be used to make both straight and curved cuts in a wide variety of materials, including wood, particleboard, plywood, plastic, metal, even ceramic tile. There is also way more than those, but those are just the basics or common things. Hope this helps!
Answer:
d²x/dt² = - 4dx/dt - 4x is the required differential equation.
Explanation:
Since the spring force F = kx where k is the spring constant and x its extension = 2.45 equals the weight of the 4 kg mass,
F = mg
kx = mg
k = mg/x
= 4 kg × 9.8 m/s²/2.45 m
= 39.2 kgm/s²/2.45 m
= 16 N/m
Now the drag force f = 16v where v is the velocity of the mass.
We now write an equation of motion for the forces on the mass. So,
F + f = ma (since both the drag force and spring force are in the same direction)where a = the acceleration of the mass
-kx - 16v = 4a
-16x - 16v = 4a
16x + 16v = -4a
4x + 4v = -a where v = dx/dt and a = d²x/dt²
4x + 4dx/dt = -d²x/dt²
d²x/dt² = - 4dx/dt - 4x which is the required differential equation
So this is dealing with the conservation of energy. So you set kinetic energy equal to potential energy, so it looks like this:
1/2mv^2=mgh. The m's cancel out, so it is 1/2v^2=gh.
To find out what the height h is, divide g on both sides, so...
h=0.5v^2/g. v=22m/s, g=9.81m/s^2, so h=(0.5)(22^2)/(9.81)=24.67m
