Griffiths Daniel
04/05/2024 · High School
Where \( v \) is the final velocity (in \( \mathrm{m} / \mathrm{s} \) ), \( u \) is the initial velocity (in \( \mathrm{m} / \mathrm{s} \) ), \( a \) is the acceleration (in \( \mathrm{m} / \mathrm{s}^{2} \) ) and \( s \) is the distance (in meters). Find \( v \) when \( u \) is \( 8 \mathrm{~m} / \mathrm{s}, a \) is \( 3 \mathrm{~m} / \mathrm{s}^{2} \), and \( s \) is 19 meters. A. \( \sqrt{130} \mathrm{~m} \) B. 13 m C. \( \sqrt{178} \mathrm{~m} \) D. 15 m
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the final velocity \( v \), we can use the kinematic equation:
\[
v^2 = u^2 + 2as
\]
where:
- \( u = 8 \, \mathrm{m/s} \) (initial velocity),
- \( a = 3 \, \mathrm{m/s}^2 \) (acceleration),
- \( s = 19 \, \mathrm{m} \) (distance).
Now, we can substitute the values into the equation:
1. Calculate \( u^2 \):
\[
u^2 = (8 \, \mathrm{m/s})^2 = 64 \, \mathrm{m}^2/\mathrm{s}^2
\]
2. Calculate \( 2as \):
\[
2as = 2 \times 3 \, \mathrm{m/s}^2 \times 19 \, \mathrm{m} = 6 \, \mathrm{m/s}^2 \times 19 \, \mathrm{m} = 114 \, \mathrm{m}^2/\mathrm{s}^2
\]
3. Now, substitute these values into the kinematic equation:
\[
v^2 = 64 \, \mathrm{m}^2/\mathrm{s}^2 + 114 \, \mathrm{m}^2/\mathrm{s}^2 = 178 \, \mathrm{m}^2/\mathrm{s}^2
\]
4. Finally, take the square root to find \( v \):
\[
v = \sqrt{178} \, \mathrm{m/s}
\]
Thus, the final velocity \( v \) is \( \sqrt{178} \, \mathrm{m/s} \).
The correct answer is:
C. \( \sqrt{178} \mathrm{~m} \)
Quick Answer
The final velocity \( v \) is \( \sqrt{178} \, \mathrm{m/s} \).
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