Answer:
The average acceleration of the car is 2.143 meters per square second.
Explanation:
Let assume that car accelerates uniformly, in that case, we can obtain the value of acceleration by using the following equation of motion:
![v = v_{o}+a\cdot t](https://tex.z-dn.net/?f=v%20%3D%20v_%7Bo%7D%2Ba%5Ccdot%20t)
Where:
- Initial velocity, measured in meters per second.
- Final velocity, measured in meters per second.
- Acceleration, measured in meters per square second.
- Time, measured in seconds.
Now, we clear acceleration within expression:
![a = \frac{v-v_{o}}{t}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bv-v_%7Bo%7D%7D%7Bt%7D)
Initial and final velocities are now converted from kilometers per hour into meters per second:
![v_{o} = \left(108\,\frac{km}{h} \right)\cdot \left(1000\,\frac{m}{km} \right)\cdot \left(\frac{1}{3600}\,\frac{h}{s} \right)](https://tex.z-dn.net/?f=v_%7Bo%7D%20%3D%20%5Cleft%28108%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20%5Cleft%281000%5C%2C%5Cfrac%7Bm%7D%7Bkm%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B3600%7D%5C%2C%5Cfrac%7Bh%7D%7Bs%7D%20%20%5Cright%29)
![v_{o} = 30\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bo%7D%20%3D%2030%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
![v = \left(135\,\frac{km}{h} \right)\cdot \left(1000\,\frac{m}{km} \right)\cdot \left(\frac{1}{3600}\,\frac{h}{s} \right)](https://tex.z-dn.net/?f=v%20%3D%20%5Cleft%28135%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20%5Cleft%281000%5C%2C%5Cfrac%7Bm%7D%7Bkm%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B3600%7D%5C%2C%5Cfrac%7Bh%7D%7Bs%7D%20%20%5Cright%29)
![v = 37.5\,\frac{m}{s}](https://tex.z-dn.net/?f=v%20%3D%2037.5%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
If we know that
, then, the average acceleration of the car is:
![a = \frac{37.5\,\frac{m}{s}-30\,\frac{m}{s} }{3.5\,s}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B37.5%5C%2C%5Cfrac%7Bm%7D%7Bs%7D-30%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B3.5%5C%2Cs%7D)
![a = 2.143\,\frac{m}{s^{2}}](https://tex.z-dn.net/?f=a%20%3D%202.143%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
The average acceleration of the car is 2.143 meters per square second.