A car initially at rest accelerates at 10m/s^2. The car’s speed after it has traveled 25 meters is most nearly… A.) 0.0m/s B.)10.0m/s C.) 22.0m/s D.) 25.0m/s
See Answers
Get the Answer.AI App
Solve problem with AI
Best Answer

The car traverses a distance [tex]x[/tex] after time [tex]t[/tex] according to


where [tex]a[/tex] is its acceleration, 10 m/s^2. The time it takes for the car to travel 25 m is

[tex]25\,\mathrm m=\left(5\dfrac{\rm m}{\mathrm s^2}\right)t^2\implies t=\sqrt 5\,\mathrm s[/tex]

5 is pretty close to 4, so we can approximate the square root of 5 by 2. Then the car's velocity [tex]v[/tex] after 2 s of travel is given by

[tex]v=\left(10\dfrac{\rm m}{\mathrm s^2}\right)(2\,\mathrm s)\approx20\dfrac{\rm m}{\rm s}[/tex]

which makes C the most likely answer.

Recommend videos
You might be interested in...
Explore more...
Get the Answer.AI App
Solve problem with AI