Velocity is directly proportional to Time.
Slope of a curve Y plotted against X is mathematically given as
![slope = \frac{dy}{dx}](https://tex.z-dn.net/?f=slope%20%3D%20%5Cfrac%7Bdy%7D%7Bdx%7D)
now here we can see that if similarly graph is plotted against distance and time then slope is given as
![slope = \frac{dx}{dt}](https://tex.z-dn.net/?f=slope%20%3D%20%5Cfrac%7Bdx%7D%7Bdt%7D)
here we can say that above is ratio of small distance and very small interval of time.
so here we can say that this ratio of distance and time for very small interval of time is known as instantaneous speed of the object which is falling freely under gravity.
So here slope of the graph will represent the speed at a given instant.
Answer:
r= 98.3 mm
Explanation:
For rim
R= 0.209 m
M= 4.32 kg
For rods
m= 7.37 kg
L= 2 R= 2 x 0.209 = 0.418 m
The Total moment of inertia of the wagon
I=MR²+2 x 1/12 m L²
Now by putting the values
![I=4.32\times 0.209^2+2\times \dfrac{1}{12}\times 7.73\times 0.418^2\ kg.m^2](https://tex.z-dn.net/?f=I%3D4.32%5Ctimes%200.209%5E2%2B2%5Ctimes%20%5Cdfrac%7B1%7D%7B12%7D%5Ctimes%207.73%5Ctimes%200.418%5E2%5C%20kg.m%5E2)
I=0.413 kg.m²
For disk:
t= 0.0462 m
Density ρ = 5990 kg/m³
Lets take r is the radius of disk
So the mass of the disc
m'=ρ πr² t
The moment of inertia of disc
I'=1/2 m'r²
I'=1/2 x r² x ρ πr² t
Given that
I = I'
1/2 x r² x ρ πr² t = 0.413 kg.m²
1/2 x r³ x ρ π t = 0.413
r³ x ρ π t = 0.826
![r^3=\dfrac{0.826}{\pi \times 5990 \times 0.0462}](https://tex.z-dn.net/?f=r%5E3%3D%5Cdfrac%7B0.826%7D%7B%5Cpi%20%5Ctimes%205990%20%5Ctimes%200.0462%7D)
r³=0.00095
r=0.0983 m
r= 98.3 mm
We know that speed is a scalar unit while velocity is a vector. The signs are mostly concerned with the magnitude that the car should travel in, the direction is not as important.
Hope I helped :)
![1.984 \times 10^{-11} \mathrm{N} \text { is the force of gravity exerted on the jar of pickles. }](https://tex.z-dn.net/?f=1.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D%20%5Ctext%20%7B%20is%20the%20force%20of%20gravity%20exerted%20on%20the%20jar%20of%20pickles.%20%7D)
<u>Explanation</u>:
According to Newton's third law that each force has an equal and opposite reaction force in this case both of the jars will exert the same force an each other
. The force is given by
![\mathrm{F}=\frac{G \times M_{1} \times M_{2}}{r^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7BG%20%5Ctimes%20M_%7B1%7D%20%5Ctimes%20M_%7B2%7D%7D%7Br%5E%7B2%7D%7D)
Where, F = force,
,
,
and Distance(r) = 0.42 m.
Substitute the values in the formula.
![\mathrm{F}=\frac{6.67 \times 10^{-11} \times 0.17 \times 0.31}{0.42^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7B6.67%20%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%200.17%20%5Ctimes%200.31%7D%7B0.42%5E%7B2%7D%7D)
![\mathrm{F}=\frac{3.51 \times 10^{-12}}{0.176}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7B3.51%20%5Ctimes%2010%5E%7B-12%7D%7D%7B0.176%7D)
![\mathrm{F}=1.984 \times 10^{-11} \mathrm{N}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D1.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D)
![\text { The force of gravity exerted on the jar of pickles is } 1.984 \times 10^{-11} \mathrm{N} \text { . }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20force%20of%20gravity%20exerted%20on%20the%20jar%20of%20pickles%20is%20%7D%201.984%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D%20%5Ctext%20%7B%20.%20%7D)