Answer :
To find the stopping distance of a car traveling at 35 mph, we will use a specific formula for calculating stopping distances. The formula is:
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where [tex]\( v \)[/tex] is the velocity in mph and [tex]\( f \)[/tex] represents the effective friction coefficient, which is influenced by factors like road conditions. In this case, we'll assume a typical friction coefficient for a dry road, which is around [tex]\( f = 0.7 \)[/tex].
Let's calculate the stopping distance step-by-step:
1. Identify the given values:
- Velocity, [tex]\( v = 35 \)[/tex] mph
- Friction coefficient, [tex]\( f = 0.7 \)[/tex]
2. Substitute these values into the formula:
[tex]\[
a(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]
3. Calculate the values:
- First, calculate [tex]\( (35)^2 = 1225 \)[/tex]
- Multiply this by 2.15, giving [tex]\( 2.15 \times 1225 = 2637.5 \)[/tex]
- Then, multiply 64.4 by 0.7, giving [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex]
4. Finally, divide the results:
[tex]\[
a(35) = \frac{2637.5}{45.08}
\][/tex]
5. Calculate and round to an appropriate level of precision:
- [tex]\( a(35) \approx 58.42 \)[/tex] feet
Thus, the stopping distance for a car traveling at 35 mph is approximately 58.42 feet.
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where [tex]\( v \)[/tex] is the velocity in mph and [tex]\( f \)[/tex] represents the effective friction coefficient, which is influenced by factors like road conditions. In this case, we'll assume a typical friction coefficient for a dry road, which is around [tex]\( f = 0.7 \)[/tex].
Let's calculate the stopping distance step-by-step:
1. Identify the given values:
- Velocity, [tex]\( v = 35 \)[/tex] mph
- Friction coefficient, [tex]\( f = 0.7 \)[/tex]
2. Substitute these values into the formula:
[tex]\[
a(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]
3. Calculate the values:
- First, calculate [tex]\( (35)^2 = 1225 \)[/tex]
- Multiply this by 2.15, giving [tex]\( 2.15 \times 1225 = 2637.5 \)[/tex]
- Then, multiply 64.4 by 0.7, giving [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex]
4. Finally, divide the results:
[tex]\[
a(35) = \frac{2637.5}{45.08}
\][/tex]
5. Calculate and round to an appropriate level of precision:
- [tex]\( a(35) \approx 58.42 \)[/tex] feet
Thus, the stopping distance for a car traveling at 35 mph is approximately 58.42 feet.
