Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Let's break down the car's journey into three distinct phases and calculate the distance covered in each phase. Finally, we'll sum all the distances for the total distance travelled.
### Phase 1: Acceleration from 0 to 20 m/s in 4 seconds
1. Initial velocity (\( u_1 \)): 0 m/s
2. Final velocity (\( v_1 \)): 20 m/s
3. Time (\( t_1 \)): 4 seconds
To find the acceleration (\( a_1 \)) during this phase, we can use the equation:
[tex]\[ a_1 = \frac{v_1 - u_1}{t_1} = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{4 \, \text{s}} = 5 \, \text{m/s}^2 \][/tex]
Now, using the formula for distance (\( s_1 \)):
[tex]\[ s_1 = u_1 t_1 + \frac{1}{2}a_1 t_1^2 \][/tex]
Substituting in the known values:
[tex]\[ s_1 = 0 \times 4 + \frac{1}{2} \times 5 \times 4^2 \][/tex]
[tex]\[ s_1 = 0 + \frac{1}{2} \times 5 \times 16 \][/tex]
[tex]\[ s_1 = 0 + 40 \][/tex]
[tex]\[ s_1 = 40 \, \text{meters} \][/tex]
### Phase 2: Constant speed at 20 m/s for 5 seconds
1. Velocity (\( v_2 \)): 20 m/s
2. Time (\( t_2 \)): 5 seconds
Distance (\( s_2 \)) in this phase can be found using the formula:
[tex]\[ s_2 = v_2 t_2 \][/tex]
Substituting the values:
[tex]\[ s_2 = 20 \, \text{m/s} \times 5 \, \text{s} \][/tex]
[tex]\[ s_2 = 100 \, \text{meters} \][/tex]
### Phase 3: Deceleration from 20 m/s to 0 in 3 seconds
1. Initial velocity (\( u_3 \)): 20 m/s
2. Final velocity (\( v_3 \)): 0 m/s
3. Time (\( t_3 \)): 3 seconds
To find the deceleration (\( a_3 \)):
[tex]\[ a_3 = \frac{v_3 - u_3}{t_3} = \frac{0 \, \text{m/s} - 20 \, \text{m/s}}{3 \, \text{s}} = -\frac{20}{3} \, \text{m/s}^2 \approx -6.67 \, \text{m/s}^2 \][/tex]
Now, using the formula for the distance (\( s_3 \)):
[tex]\[ s_3 = u_3 t_3 + \frac{1}{2} a_3 t_3^2 \][/tex]
Substituting the values:
[tex]\[ s_3 = 20 \times 3 + \frac{1}{2} \times \left(-\frac{20}{3}\right) \times 3^2 \][/tex]
[tex]\[ s_3 = 60 + \frac{1}{2} \times -20 \times 3 \][/tex]
[tex]\[ s_3 = 60 - 30 \][/tex]
[tex]\[ s_3 = 30 \, \text{meters} \][/tex]
### Total Distance Travelled
The total distance travelled by the car is the sum of the distances covered in all three phases:
[tex]\[ \text{Total Distance} = s_1 + s_2 + s_3 \][/tex]
Substitute the values:
[tex]\[ \text{Total Distance} = 40 \, \text{m} + 100 \, \text{m} + 30 \, \text{m} \][/tex]
[tex]\[ \text{Total Distance} = 170 \, \text{meters} \][/tex]
Thus, the total distance travelled by the car is 170 meters.
### Phase 1: Acceleration from 0 to 20 m/s in 4 seconds
1. Initial velocity (\( u_1 \)): 0 m/s
2. Final velocity (\( v_1 \)): 20 m/s
3. Time (\( t_1 \)): 4 seconds
To find the acceleration (\( a_1 \)) during this phase, we can use the equation:
[tex]\[ a_1 = \frac{v_1 - u_1}{t_1} = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{4 \, \text{s}} = 5 \, \text{m/s}^2 \][/tex]
Now, using the formula for distance (\( s_1 \)):
[tex]\[ s_1 = u_1 t_1 + \frac{1}{2}a_1 t_1^2 \][/tex]
Substituting in the known values:
[tex]\[ s_1 = 0 \times 4 + \frac{1}{2} \times 5 \times 4^2 \][/tex]
[tex]\[ s_1 = 0 + \frac{1}{2} \times 5 \times 16 \][/tex]
[tex]\[ s_1 = 0 + 40 \][/tex]
[tex]\[ s_1 = 40 \, \text{meters} \][/tex]
### Phase 2: Constant speed at 20 m/s for 5 seconds
1. Velocity (\( v_2 \)): 20 m/s
2. Time (\( t_2 \)): 5 seconds
Distance (\( s_2 \)) in this phase can be found using the formula:
[tex]\[ s_2 = v_2 t_2 \][/tex]
Substituting the values:
[tex]\[ s_2 = 20 \, \text{m/s} \times 5 \, \text{s} \][/tex]
[tex]\[ s_2 = 100 \, \text{meters} \][/tex]
### Phase 3: Deceleration from 20 m/s to 0 in 3 seconds
1. Initial velocity (\( u_3 \)): 20 m/s
2. Final velocity (\( v_3 \)): 0 m/s
3. Time (\( t_3 \)): 3 seconds
To find the deceleration (\( a_3 \)):
[tex]\[ a_3 = \frac{v_3 - u_3}{t_3} = \frac{0 \, \text{m/s} - 20 \, \text{m/s}}{3 \, \text{s}} = -\frac{20}{3} \, \text{m/s}^2 \approx -6.67 \, \text{m/s}^2 \][/tex]
Now, using the formula for the distance (\( s_3 \)):
[tex]\[ s_3 = u_3 t_3 + \frac{1}{2} a_3 t_3^2 \][/tex]
Substituting the values:
[tex]\[ s_3 = 20 \times 3 + \frac{1}{2} \times \left(-\frac{20}{3}\right) \times 3^2 \][/tex]
[tex]\[ s_3 = 60 + \frac{1}{2} \times -20 \times 3 \][/tex]
[tex]\[ s_3 = 60 - 30 \][/tex]
[tex]\[ s_3 = 30 \, \text{meters} \][/tex]
### Total Distance Travelled
The total distance travelled by the car is the sum of the distances covered in all three phases:
[tex]\[ \text{Total Distance} = s_1 + s_2 + s_3 \][/tex]
Substitute the values:
[tex]\[ \text{Total Distance} = 40 \, \text{m} + 100 \, \text{m} + 30 \, \text{m} \][/tex]
[tex]\[ \text{Total Distance} = 170 \, \text{meters} \][/tex]
Thus, the total distance travelled by the car is 170 meters.
I spent a while on this, not sure if it’s correct but here:
To determine the total distance traveled by the car, we'll break the motion into three phases: acceleration, constant speed, and deceleration.
Phase 1: Acceleration
- Initial velocity (u1): 0 m/s
- Final velocity (v1): 20 m/s
- Time (t1): 4 seconds
Acceleration (a1) can be calculated as:
a1 = (v1 - u1) / t1
a1 = (20 m/s - 0 m/s) / 4 s
a1 = 5 m/s²
Distance (d1) during this phase can be calculated using the formula:
d1 = u1 * t1 + 0.5 * a1 * t1²
d1 = 0 * 4 + 0.5 * 5 * 4²
d1 = 0 + 0.5 * 5 * 16
d1 = 40 meters
Phase 2: Constant speed
- Speed (v2): 20 m/s
- Time (t2): 5 seconds
Distance (d2) during this phase can be calculated as:
d2 = v2 * t2
d2 = 20 m/s * 5 s
d2 = 100 meters
Phase 3: Deceleration
- Initial velocity (u3): 20 m/s
- Final velocity (v3): 0 m/s
- Time (t3): 3 seconds
Deceleration (a3) can be calculated as:
a3 = (v3 - u3) / t3
a3 = (0 m/s - 20 m/s) / 3 s
a3 = -20/3 m/s²
Distance (d3) during this phase can be calculated using the formula:
d3 = u3 * t3 + 0.5 * a3 * t3²
d3 = 20 * 3 + 0.5 * (-20/3) * 3²
d3 = 60 - 0.5 * 20 * 3
d3 = 60 - 30
d3 = 30 meters
Total distance traveled is the sum of the distances for all three phases:
Total distance = d1 + d2 + d3
Total distance = 40 meters + 100 meters + 30 meters
Total distance = 170 meters
The total distance traveled by the car is 170 meters.
To determine the total distance traveled by the car, we'll break the motion into three phases: acceleration, constant speed, and deceleration.
Phase 1: Acceleration
- Initial velocity (u1): 0 m/s
- Final velocity (v1): 20 m/s
- Time (t1): 4 seconds
Acceleration (a1) can be calculated as:
a1 = (v1 - u1) / t1
a1 = (20 m/s - 0 m/s) / 4 s
a1 = 5 m/s²
Distance (d1) during this phase can be calculated using the formula:
d1 = u1 * t1 + 0.5 * a1 * t1²
d1 = 0 * 4 + 0.5 * 5 * 4²
d1 = 0 + 0.5 * 5 * 16
d1 = 40 meters
Phase 2: Constant speed
- Speed (v2): 20 m/s
- Time (t2): 5 seconds
Distance (d2) during this phase can be calculated as:
d2 = v2 * t2
d2 = 20 m/s * 5 s
d2 = 100 meters
Phase 3: Deceleration
- Initial velocity (u3): 20 m/s
- Final velocity (v3): 0 m/s
- Time (t3): 3 seconds
Deceleration (a3) can be calculated as:
a3 = (v3 - u3) / t3
a3 = (0 m/s - 20 m/s) / 3 s
a3 = -20/3 m/s²
Distance (d3) during this phase can be calculated using the formula:
d3 = u3 * t3 + 0.5 * a3 * t3²
d3 = 20 * 3 + 0.5 * (-20/3) * 3²
d3 = 60 - 0.5 * 20 * 3
d3 = 60 - 30
d3 = 30 meters
Total distance traveled is the sum of the distances for all three phases:
Total distance = d1 + d2 + d3
Total distance = 40 meters + 100 meters + 30 meters
Total distance = 170 meters
The total distance traveled by the car is 170 meters.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
