Question

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

Answer 1

The car traverses a distance $x$ after time $t$ according to

$x=\dfrac12at^2$

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

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

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

$v=\left(10\dfrac{\rm m}{\mathrm s^2}\right)(2\,\mathrm s)\approx20\dfrac{\rm m}{\rm s}$

which makes C the most likely answer.