A drag racer starts her car from rest and accelerates at 9.2 m/s2 for the entire distance of 631 m.
How long did it take the car to travel this distance?
Answer in units of s
To find the time it takes for the car to travel the given distance, we can use the following equation:
d = 0.5 * a * t^2
Where:
d = distance (631 m)
a = acceleration (9.2 m/s^2)
t = time
Rearranging the equation to solve for time:
t^2 = (2 * d) / a
Substituting the values:
t^2 = (2 * 631 m) / 9.2 m/s^2
t^2 = 136.9565
Taking the square root of both sides to find time:
t = √(136.9565)
t ≈ 11.70 s
Therefore, it took the drag racer approximately 11.70 seconds to travel a distance of 631 meters.
To find the time it took for the car to travel 631 m, we can use the equation of motion:
\[s = ut + \frac{1}{2}at^2\]
where:
- \(s\) is the distance traveled (631 m in this case)
- \(u\) is the initial velocity (0 m/s if the car starts from rest)
- \(a\) is the acceleration (9.2 m/s\(^2\) in this case)
- \(t\) is the time taken to travel the distance
Since the car starts from rest, the initial velocity (\(u\)) is 0 m/s. We can now rearrange the equation to solve for \(t\):
\[s = \frac{1}{2}at^2\]
Plugging in the given values, we have:
\[631 = \frac{1}{2} \times 9.2 \times t^2\]
Simplifying,
\[t^2 = \frac{631}{\frac{1}{2} \times 9.2} = \frac{631 \times 2}{9.2}\]
\[t^2 = \frac{1262}{9.2}\]
To find \(t\), we take the square root of both sides:
\[t = \sqrt{\frac{1262}{9.2}}\]
Using a calculator, we find that \(t \approx 11.58\) seconds (rounded to two decimal places).
Therefore, it took approximately 11.58 seconds to travel the distance of 631 m.