Question

Physics

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

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Best Answer

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

[tex]x=\dfrac12at^2[/tex]

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.