Answer:
15.8640053791 s
392.780107582 m
29.5184032275 m/s
Explanation:
0 denotes initial
x denotes displacement
c denotes car
t denotes truck
r denotes rear
![x_0_{cr}=-49.5\ m](https://tex.z-dn.net/?f=x_0_%7Bcr%7D%3D-49.5%5C%20m)
![a_c=0.6\ m/s^2](https://tex.z-dn.net/?f=a_c%3D0.6%5C%20m%2Fs%5E2)
![x_0_{t}=0](https://tex.z-dn.net/?f=x_0_%7Bt%7D%3D0)
![v_0_{c}=v_0_{t}](https://tex.z-dn.net/?f=v_0_%7Bc%7D%3Dv_0_%7Bt%7D)
For the car
![x_c=x_0+v_0_{c}t+\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=x_c%3Dx_0%2Bv_0_%7Bc%7Dt%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
The displacement of the truck will be
![x_t=v_tt](https://tex.z-dn.net/?f=x_t%3Dv_tt)
From the above two equations we get
![x_c-x_t=x_0+v_0_{c}+\dfrac{1}{2}at-v_{t}t=26\\\Rightarrow 26=x_0+\dfrac{1}{2}at^2\\\Rightarrow 26+49.5=\dfrac{1}{2}0.6t^2\\\Rightarrow t=\sqrt{\dfrac{2(26+49.5)}{0.6}}\\\Rightarrow t=15.8640053791\ s](https://tex.z-dn.net/?f=x_c-x_t%3Dx_0%2Bv_0_%7Bc%7D%2B%5Cdfrac%7B1%7D%7B2%7Dat-v_%7Bt%7Dt%3D26%5C%5C%5CRightarrow%2026%3Dx_0%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%2026%2B49.5%3D%5Cdfrac%7B1%7D%7B2%7D0.6t%5E2%5C%5C%5CRightarrow%20t%3D%5Csqrt%7B%5Cdfrac%7B2%2826%2B49.5%29%7D%7B0.6%7D%7D%5C%5C%5CRightarrow%20t%3D15.8640053791%5C%20s)
The time taken is 15.8640053791 s
![x-x_0=v_{0}_{c}t+\dfrac{1}{2}at^2\\\Rightarrow x-x_0=20\times 15.8640053791+\dfrac{1}{2}0.6\times 15.8640053791^2\\\Rightarrow x-x_0=392.780107582\ m](https://tex.z-dn.net/?f=x-x_0%3Dv_%7B0%7D_%7Bc%7Dt%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%20x-x_0%3D20%5Ctimes%2015.8640053791%2B%5Cdfrac%7B1%7D%7B2%7D0.6%5Ctimes%2015.8640053791%5E2%5C%5C%5CRightarrow%20x-x_0%3D392.780107582%5C%20m)
The distance the car travels is 392.780107582 m
![v=v_0+at\\\Rightarrow v=20+0.6\times 15.8640053791\\\Rightarrow v=29.5184032275\ m/s](https://tex.z-dn.net/?f=v%3Dv_0%2Bat%5C%5C%5CRightarrow%20v%3D20%2B0.6%5Ctimes%2015.8640053791%5C%5C%5CRightarrow%20v%3D29.5184032275%5C%20m%2Fs)
The velocity of the car is 29.5184032275 m/s
Answer:
![\boxed {\boxed {\sf v= 4.5 \ m/s}}](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Cboxed%20%7B%5Csf%20v%3D%204.5%20%5C%20m%2Fs%7D%7D)
Explanation:
The formula for momentum is:
![p=mv](https://tex.z-dn.net/?f=p%3Dmv)
(<em>p</em> is momentum, <em>m</em> is mass, and <em>v </em>is velocity)
Let's rearrange the formula for velocity, or v.
![\frac{p}{m} =v](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7Bm%7D%20%3Dv)
Velocity can be found by dividing the momentum by the mass.
The momentum is 180 kilograms meter per second. The mass of the boy is 40 kilograms.
![p=180 \ kg*m/s \\m=40 kg](https://tex.z-dn.net/?f=p%3D180%20%5C%20kg%2Am%2Fs%20%5C%5Cm%3D40%20%20kg)
Substitute the values into the formula.
![v=\frac{180 \ kg*m/s}{40 \ kg}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B180%20%5C%20kg%2Am%2Fs%7D%7B40%20%5C%20kg%7D)
Divide. Note that the kilograms or "kg" will cancel each other out.
![v=\frac{180 \ m/s}{40 }](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B180%20%5C%20m%2Fs%7D%7B40%20%7D)
![v= 4.5 \ m/s](https://tex.z-dn.net/?f=v%3D%204.5%20%5C%20m%2Fs)
The velocity of the boy is <u>4.5 meters per second.</u>
We have no idea what the illustration shows, because you neglected to let us see it.
The most common reason for light to bend is refraction, normally caused by a difference in the <em>speed</em> of the light in two different media ... the one it comes out of and the one it goes into.
Answer:
A
![\epsilon_{max} = 0.774 \ V](https://tex.z-dn.net/?f=%5Cepsilon_%7Bmax%7D%20%20%3D%200.774%20%5C%20%20V)
B
![wt = 0^o](https://tex.z-dn.net/?f=wt%20%20%3D%20%200%5Eo)
Explanation:
From the question we are told that
The length of the side is ![l = 16.0 \ cm = 0.16 \ m](https://tex.z-dn.net/?f=l%20%20%3D%20%2016.0%20%5C%20cm%20%20%3D%200.16%20%5C%20m)
The number of turns is ![N = 29 \ turns](https://tex.z-dn.net/?f=N%20%3D%2029%20%20%5C%20turns)
The magnetic field is ![B = 83.0 mT = 83 *10^{-3} \ T](https://tex.z-dn.net/?f=B%20%3D%20%2083.0%20mT%20%20%3D%20%2083%20%2A10%5E%7B-3%7D%20%5C%20T)
The angular speed is ![w = 1.20 * 10^2 rev/min = \frac{1.20 *10^2 * 2\pi}{60 } = 12.6 \ rad/s](https://tex.z-dn.net/?f=w%20%20%3D%20%201.20%20%2A%2010%5E2%20%20rev%2Fmin%20%3D%20%20%5Cfrac%7B1.20%20%2A10%5E2%20%2A%20%202%5Cpi%7D%7B60%20%7D%20%3D%2012.6%20%5C%20%20rad%2Fs)
Generally the area is ![A = l^2](https://tex.z-dn.net/?f=A%20%3D%20%20l%5E2)
Generally the induced emf is mathematically represented as
![\epsilon = N * w * B * A * cos(wt)](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%20%20N%20%2A%20w%20%20%2A%20%20B%20%20%2A%20%20A%20%20%2A%20cos%28wt%29)
At maximum ![cos(wt) = 1](https://tex.z-dn.net/?f=cos%28wt%29%20%3D%20%201)
So
![\epsilon_{max} = N * w * B * A](https://tex.z-dn.net/?f=%5Cepsilon_%7Bmax%7D%20%20%3D%20%20N%20%2A%20w%20%20%2A%20%20B%20%20%2A%20%20A)
![\epsilon_{max} = 29 * 12.6 * 83*10^{-3}* (l^2)](https://tex.z-dn.net/?f=%5Cepsilon_%7Bmax%7D%20%20%3D%2029%20%20%2A%20%2012.6%20%2A%20%2083%2A10%5E%7B-3%7D%2A%20%28l%5E2%29)
=> ![\epsilon_{max} = 29 * 12.6 * 83*10^{-3}* ((0.16)^2)](https://tex.z-dn.net/?f=%5Cepsilon_%7Bmax%7D%20%20%3D%2029%20%20%2A%20%2012.6%20%2A%20%2083%2A10%5E%7B-3%7D%2A%20%28%280.16%29%5E2%29)
=> ![\epsilon_{max} = 0.774 \ V](https://tex.z-dn.net/?f=%5Cepsilon_%7Bmax%7D%20%20%3D%200.774%20%5C%20%20V)
At maximum emf
![cos (wt) = 1](https://tex.z-dn.net/?f=cos%20%28wt%29%20%20%3D%20%201)
=> ![(wt) = cos^{-1} (1)](https://tex.z-dn.net/?f=%28wt%29%20%20%3D%20%20cos%5E%7B-1%7D%20%281%29)
=> ![wt = 0^o](https://tex.z-dn.net/?f=wt%20%20%3D%20%200%5Eo)