You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and begin decelerating at 3.7 m/s2 .
part A=How far do you travel before stopping?
part B= When you have traveled only half the distance in part A, is your speed 7.0 m/s , greater than 7.0 m/s , or less than 7.0 m/s ?
how did you get 8.5
The only wrong with his problem is that he accidentally did 3.2 x 2 = 7.4. It should be 6.4 hence your answer should be 31 m.
Well, well, well, seems like you've got yourself in a bit of a pickle there, my friend! Let me give you a hand (or a clown shoe) to figure this out.
PART A: To calculate how far you travel before stopping, we can use the equation of motion: v² = u² + 2as. In this case, u = 12.0 m/s, a = -3.7 m/s^2 (negative because it's decelerating), and v = 0 m/s (since you're stopping). So, let's plug in the numbers:
0² = 12.0² + 2(-3.7)s
Now, let's solve for s, which represents the distance traveled:
s = (0² - 12.0²) / (2(-3.7))
After doing the math, you'll find that the distance you travel before stopping is approximately 10.84 meters. So, keep your eyes peeled for rolling balls!
PART B: Now, when you've traveled only half the distance calculated in Part A (which is about 5.42 meters), we need to find the speed. To do this, we can use the equation v² = u² + 2as once again, but this time we know the distance (a), initial velocity (u), and acceleration (a). The final velocity (v) will be the mystery we're trying to solve. So, let's rewrite the equation:
v² = 12.0² + 2(-3.7)(5.42)
Let's put on our laughter glasses and solve for v!
v² = 144 + 2(-3.7)(5.42)
v² = 144 - 40.648
v² ≈ 103.352
v ≈ √103.352
v ≈ 10.17 meters per second
Well, well, well, it seems when you've traveled only half the distance, your speed will be approximately 10.17 meters per second. So, it's greater than 7.0 m/s! Keep those brakes handy, my friend, and make sure you don't miss out on any clown shows while you're at it. Stay safe!
To answer part A of the question, you need to calculate the distance traveled before coming to a stop. This can be done using the formula:
\[d = \frac{{v^2 - u^2}}{{2a}}\]
Where:
- d represents the distance traveled
- v represents the final velocity (which is 0 m/s since you come to a stop)
- u represents the initial velocity (12.0 m/s)
- a represents the acceleration (deceleration in this case, which is -3.7 m/s²)
Substituting the values into the formula, we get:
\[d = \frac{{0^2 - (12.0)^2}}{{2 \cdot (-3.7)}}\]
Simplifying further:
\[d = \frac{{-144}}{{-7.4}} = 19.46 \, \text{m}\]
Therefore, you travel a distance of approximately 19.46 meters before stopping.
To answer part B of the question, you need to determine your speed when you have traveled only half the distance found in part A. You can calculate this using the equation:
\[v^2 = u^2 + 2ad\]
Where:
- v represents the final velocity (which is what we want to find)
- u represents the initial velocity (12.0 m/s)
- a represents the acceleration (deceleration in this case, which is -3.7 m/s²)
- d represents half of the distance traveled (half of the value found in part A, which is 19.46 m divided by 2)
Substituting the values into the formula:
\[v^2 = (12.0)^2 + 2 \cdot (-3.7) \cdot \left(\frac{{19.46}}{2}\right)\]
Simplifying further:
\[v^2 = 144 + 2 \times (-3.7) \times 9.73\]
\[v^2 = 144 - 72.34\]
\[v^2 = 71.66\]
To find v (the final velocity), we take the square root of both sides:
\[v = \sqrt{71.66} \approx 8.47 \, \text{m/s}\]
Therefore, when you have traveled only half the distance found in part A, your speed is approximately 8.47 m/s. This is greater than 7.0 m/s.
helppp please
A. V^2 = Vo^2+2a*d = 0
144-7.4d = 0.
d = 19.5 m.
B. V^2=Vo^2+2a*d = 144-7.4*(19.5/2) = 71.85
V = 8.5 m/s
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