Question
ou can use your notes from yesterday.
Question at position 1
1
Fill in the Blank
10 points
Question at position 1
A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
x = Question Blank 1 of 6
110
Vi = Question Blank 2 of 6
0
Vf = Question Blank 3 of 6
Answer
a = Question Blank 4 of 6
Answer
t = Question Blank 5 of 6
Answer
Which equation should be used? Question Blank 6 of 6
Answer
Question at position 1
1
Fill in the Blank
10 points
Question at position 1
A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
x = Question Blank 1 of 6
110
Vi = Question Blank 2 of 6
0
Vf = Question Blank 3 of 6
Answer
a = Question Blank 4 of 6
Answer
t = Question Blank 5 of 6
Answer
Which equation should be used? Question Blank 6 of 6
Answer
Answers
GPT-4o mini
To solve the problem, we can use the equations of uniformly accelerated motion. We'll start by identifying the variables given:
- Distance (x) = 110 m
- Initial velocity (Vi) = 0 m/s (starts from rest)
- Final velocity (Vf) = ?
- Acceleration (a) = ?
- Time (t) = 5.21 seconds
We can use the following kinematic equation that relates distance, initial velocity, time, and acceleration:
\[ x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \]
Since Vi = 0, the equation simplifies to:
\[ x = \frac{1}{2} a \cdot t^2 \]
Substituting the known values into the equation:
\[ 110 = \frac{1}{2} a \cdot (5.21)^2 \]
Now, calculating \( (5.21)^2 \):
\[ (5.21)^2 \approx 27.1441 \]
Substituting this value back into the equation:
\[ 110 = \frac{1}{2} a \cdot 27.1441 \]
Now, multiplying both sides by 2 to isolate \( a \):
\[ 220 = a \cdot 27.1441 \]
Now, solve for \( a \):
\[ a = \frac{220}{27.1441} \approx 8.10 \, \text{m/s}^2 \]
Now, filling in the blanks:
1. Question Blank 1 (x): **110**
2. Question Blank 2 (Vi): **0**
3. Question Blank 3 (Vf): **Compute Vf using Vf = Vi + a*t**
\[ Vf = 0 + (8.10)(5.21) \approx 42.21 \, \text{m/s} \]
4. Question Blank 4 (a): **8.10**
5. Question Blank 5 (t): **5.21**
6. Which equation should be used? **\( x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \)**
So the final answers are:
1. **110**
2. **0**
3. **42.21**
4. **8.10**
5. **5.21**
6. **\( x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \)**
- Distance (x) = 110 m
- Initial velocity (Vi) = 0 m/s (starts from rest)
- Final velocity (Vf) = ?
- Acceleration (a) = ?
- Time (t) = 5.21 seconds
We can use the following kinematic equation that relates distance, initial velocity, time, and acceleration:
\[ x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \]
Since Vi = 0, the equation simplifies to:
\[ x = \frac{1}{2} a \cdot t^2 \]
Substituting the known values into the equation:
\[ 110 = \frac{1}{2} a \cdot (5.21)^2 \]
Now, calculating \( (5.21)^2 \):
\[ (5.21)^2 \approx 27.1441 \]
Substituting this value back into the equation:
\[ 110 = \frac{1}{2} a \cdot 27.1441 \]
Now, multiplying both sides by 2 to isolate \( a \):
\[ 220 = a \cdot 27.1441 \]
Now, solve for \( a \):
\[ a = \frac{220}{27.1441} \approx 8.10 \, \text{m/s}^2 \]
Now, filling in the blanks:
1. Question Blank 1 (x): **110**
2. Question Blank 2 (Vi): **0**
3. Question Blank 3 (Vf): **Compute Vf using Vf = Vi + a*t**
\[ Vf = 0 + (8.10)(5.21) \approx 42.21 \, \text{m/s} \]
4. Question Blank 4 (a): **8.10**
5. Question Blank 5 (t): **5.21**
6. Which equation should be used? **\( x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \)**
So the final answers are:
1. **110**
2. **0**
3. **42.21**
4. **8.10**
5. **5.21**
6. **\( x = Vi \cdot t + \frac{1}{2} a \cdot t^2 \)**