Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To solve the problem of determining how long it takes for a bicycle traveling at an initial velocity of [tex]\(7.0 \, \text{m/s}\)[/tex] to come to a stop with a constant acceleration of [tex]\(-3.5 \, \text{m/s}^2\)[/tex], we'll use the kinematic equation which relates velocity, acceleration, and time.
The kinematic equation we will use is:
[tex]\[ v_f = v_i + at \][/tex]
Where:
- [tex]\(v_f\)[/tex] is the final velocity.
- [tex]\(v_i\)[/tex] is the initial velocity.
- [tex]\(a\)[/tex] is the acceleration.
- [tex]\(t\)[/tex] is the time.
Since the bicycle comes to a stop, the final velocity ([tex]\(v_f\)[/tex]) is [tex]\(0 \, \text{m/s}\)[/tex].
Given:
- [tex]\(v_i = 7.0 \, \text{m/s}\)[/tex]
- [tex]\(a = -3.5 \, \text{m/s}^2\)[/tex]
- [tex]\(v_f = 0 \, \text{m/s}\)[/tex]
Plug these values into the kinematic equation:
[tex]\[ 0 = 7.0 + (-3.5) \cdot t \][/tex]
Next, solve for time ([tex]\(t\)[/tex]):
[tex]\[ 0 = 7.0 - 3.5t \][/tex]
[tex]\[ 3.5t = 7.0 \][/tex]
[tex]\[ t = \frac{7.0}{3.5} \][/tex]
[tex]\[ t = 2.0 \, \text{s} \][/tex]
So, the time it takes for the bicycle to come to a stop is:
[tex]\[ \boxed{2.0 \, \text{s}} \][/tex]
Therefore, the correct option is:
D. [tex]\(2.0 \, \text{s}\)[/tex]
The kinematic equation we will use is:
[tex]\[ v_f = v_i + at \][/tex]
Where:
- [tex]\(v_f\)[/tex] is the final velocity.
- [tex]\(v_i\)[/tex] is the initial velocity.
- [tex]\(a\)[/tex] is the acceleration.
- [tex]\(t\)[/tex] is the time.
Since the bicycle comes to a stop, the final velocity ([tex]\(v_f\)[/tex]) is [tex]\(0 \, \text{m/s}\)[/tex].
Given:
- [tex]\(v_i = 7.0 \, \text{m/s}\)[/tex]
- [tex]\(a = -3.5 \, \text{m/s}^2\)[/tex]
- [tex]\(v_f = 0 \, \text{m/s}\)[/tex]
Plug these values into the kinematic equation:
[tex]\[ 0 = 7.0 + (-3.5) \cdot t \][/tex]
Next, solve for time ([tex]\(t\)[/tex]):
[tex]\[ 0 = 7.0 - 3.5t \][/tex]
[tex]\[ 3.5t = 7.0 \][/tex]
[tex]\[ t = \frac{7.0}{3.5} \][/tex]
[tex]\[ t = 2.0 \, \text{s} \][/tex]
So, the time it takes for the bicycle to come to a stop is:
[tex]\[ \boxed{2.0 \, \text{s}} \][/tex]
Therefore, the correct option is:
D. [tex]\(2.0 \, \text{s}\)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.