Answer:
(a) Acceleration 
(b) Distance s = 25 m
Explanation:
We have given constant force F = 2000 N
Mass of the car = 1000 kg
(a) From newton's law we know that F = ma
So 

(b) Tine is given as t = 5 sec
As the car is initially at rest so initial velocity u = 0 m/sec
From second equation of motion 
So 
Let's assume these microwaves are traveling in a vacuum, then this equation holds true:
c = fλ
c is the speed of light in a vacuum, f is the frequency, and λ is the wavelength.
Given values:
c = 3×10⁸m/s
λ = 20×10⁻³m
Plug in the values and solve for f:
3×10⁸ = f(20×10⁻³)
f = 15GHz
Choice A
Answer:
122.5 N/m
Explanation:
According to the law of conservation of energy, if there is no air resistance or frictional forces, the initial elastic potential energy of the spring toy is entirely converted into gravitational potential energy when the toy reaches the highest point.
Therefore, we can write:

where the term on the left is the initial elastic potential energy while the term on the right is the gravitational potential energy, and where
k is the spring constant
x = 0.02 m is the compression of the spring
m = 0.01 kg is the mass of the toy
h = 0.25 m is the height reached by the toy
is the acceleration due to gravity
Solving for k,

For constant acceleration along a given direction, we can relate acceleration, velocity and position with the following equation that doesn't involve time:

In this equation x is the final position, which we take to be 0. Also the initial velocity Vo is zero. Thus the equation simplifies to

Putting in v=32m/s, a=-9.81m/s^2 gives

Answer:
a) y-8 = (y₀-8)
, b) 2y -5 = (2y₀-5)
Explanation:
To solve these equations the method of direct integration is the easiest.
a) the given equation is
dy / dt = and -8
dy / y-8 = dt
We change variables
y-8 = u
dy = du
We replace and integrate
∫ du / u = ∫ dt
Ln (y-8) = t
We evaluate at the lower limits t = 0 for y = y₀
ln (y-8) - ln (y₀-8) = t-0
Let's simplify the equation
ln (y-8 / y₀-8) = t
y-8 / y₀-8 =
y-8 = (y₀-8)
b) the equation is
dy / dt = 2y -5
u = 2y -5
du = 2 dy
du / 2u = dt
We integrate
½ Ln (2y-5) = t
We evaluate at the limits
½ [ln (2y-5) - ln (2y₀-5)] = t
Ln (2y-5 / 2y₀-5) = 2t
2y -5 = (2y₀-5)
c) the equation is very similar to the previous one
u = 2y -10
du = 2 dy
∫ du / 2u = dt
ln (2y-10) = 2t
We evaluate
ln (2y-10) –ln (2y₀-10) = 2t
2y-10 = (2y₀-10)