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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LammettHash LammettHash · Answer 1 · 2019-10-08T23:07:06+02:00

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.

asuwafohjames asuwafohjames · Answer 2 · 2021-09-03T18:57:40+02:00

A car initially at rest accelerates at 10m/s^2. The car’s speed after it has traveled 25 meters is most nearly C.) 22.0 m/s

Speed: This can be defined as the rate of change of distance. The s.i unit of speed is m/s.

The question above can be solved using the formula below.

v² = u²+2as.................. Equation 1

Where v = final velocity, u = initial velocity, a = acceleration, s = distance.

From the question,

Given: u = 0 m/s ( Initially at rest), a = 10 m/s², s = 25 meters.

Substitute these values into equation 1

v² = 0²+2(10)(25)

v² = 500

v = √(500)

v = 22.36 m/s.

From the question above, the correct option is C.) 22.0 m/s.

Hence the car's speed is C.) 22.0 m/s

Learn more about speed here: https://brainly.com/question/13262646