Answer:
I believe the answer is A and D.
I am unsure of C.
Answer:
Unbalanced forces change the motion of an object. If an object is at rest and an unbalanced force pushes or pulls the object, it will move. Unbalanced forces can also change the speed or direction of an object that is already in motion.
The distance decreases as the time increases
When acceleration is constant, the average velocity is given by
![\bar v=\dfrac{v+v_0}2](https://tex.z-dn.net/?f=%5Cbar%20v%3D%5Cdfrac%7Bv%2Bv_0%7D2)
where
and
are the final and initial velocities, respectively. By definition, we also have that the average velocity is given by
![\bar v=\dfrac{\Delta x}{\Delta t}=\dfrac{x-x_0}{t-t_0}](https://tex.z-dn.net/?f=%5Cbar%20v%3D%5Cdfrac%7B%5CDelta%20x%7D%7B%5CDelta%20t%7D%3D%5Cdfrac%7Bx-x_0%7D%7Bt-t_0%7D)
where
are the final/initial displacements, and
are the final/initial times, respectively.
Take the car's starting position to be at
. Then
![\dfrac{v+v_0}2=\dfrac{x-x_0}t\implies x=x_0+\dfrac12(v+v_0)t](https://tex.z-dn.net/?f=%5Cdfrac%7Bv%2Bv_0%7D2%3D%5Cdfrac%7Bx-x_0%7Dt%5Cimplies%20x%3Dx_0%2B%5Cdfrac12%28v%2Bv_0%29t)
So we have
![x=0\,\mathrm m+\dfrac12\left(0\,\dfrac{\mathrm m}{\mathrm s}+30.0\,\dfrac{\mathrm m}{\mathrm s}\right)(7.20\,\mathrm s)=108\,\mathrm m](https://tex.z-dn.net/?f=x%3D0%5C%2C%5Cmathrm%20m%2B%5Cdfrac12%5Cleft%280%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%2B30.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29%287.20%5C%2C%5Cmathrm%20s%29%3D108%5C%2C%5Cmathrm%20m)
You also could have first found the acceleration using the equation
![v=v_0+at](https://tex.z-dn.net/?f=v%3Dv_0%2Bat)
then solve for
via
![x=x_0+v_0t+\dfrac12at^2](https://tex.z-dn.net/?f=x%3Dx_0%2Bv_0t%2B%5Cdfrac12at%5E2)
but that would have involved a bit more work, and it turns out we didn't need to know the precise value of
anyway.
Answer:
The average impact force is 12000 newtons.
Explanation:
By Impact Theorem we know that impact done by the sledge hammer on the chisel is equal to the change in the linear momentum of the former. The mathematical model that represents the situation is now described:
(1)
Where:
- Average impact force, in newtons.
- Duration of the impact, in seconds.
- Mass of the sledge hammer, in kilograms.
,
- Initial and final velocity, in meters per second.
If we know that
,
,
and
, then we estimate the average impact force is:
![\bar F = \frac{m\cdot (v_{2}-v_{1})}{\Delta t}](https://tex.z-dn.net/?f=%5Cbar%20F%20%3D%20%5Cfrac%7Bm%5Ccdot%20%20%28v_%7B2%7D-v_%7B1%7D%29%7D%7B%5CDelta%20t%7D)
![\bar F = 12000\,N](https://tex.z-dn.net/?f=%5Cbar%20F%20%3D%2012000%5C%2CN)
The average impact force is 12000 newtons.