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At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car?
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At t is equal to zero and x is equal to zero and initial stationery bl...
**Problem Statement**
A blue car starts from rest and accelerates at a constant rate of 0.2 m/s² in the positive direction of the x-axis. At t = 2 seconds, a red car traveling in an adjacent lane and in the same direction passes x = 0 with a speed of 8.0 m/s and constant acceleration of 3.0 m/s². Find the time at which the red car passes the blue car.
**Solution**
To solve the problem, we need to determine the position of both cars as a function of time and then find the time at which their positions are equal. We can use the following kinematic equations to determine the position of each car:
- x = x₀ + v₀t + ½at²
where x is the position of the car at time t, x₀ is the initial position, v₀ is the initial velocity, a is the acceleration, and t is the time.
**Calculations for Blue Car**
- Given: x₀ = 0, v₀ = 0, a = 0.2 m/s²
- x = 0 + 0t + ½(0.2)t²
- x = 0.1t²
**Calculations for Red Car**
- Given: x₀ = 0, v₀ = 8.0 m/s, a = 3.0 m/s²
- x = 0 + 8.0t + ½(3.0)t²
- x = 8.0t + 1.5t²
**Finding the Time at which Red Car Passes Blue Car**
To find the time at which the red car passes the blue car, we need to set their positions equal to each other and solve for t.
- 0.1t² = 8.0t + 1.5t²
- 0.4t² - 8.0t = 0
- t(0.4t - 8.0) = 0
This equation has two solutions: t = 0 and t = 20 seconds. The first solution corresponds to the time when both cars are at x = 0, which is not the time when the red car passes the blue car. Therefore, the time at which the red car passes the blue car is:
- t = 20 seconds
**Conclusion**
In conclusion, the red car will pass the blue car after 20 seconds. At this time, the position of the blue car is x = 0.1(20)² = 40 meters, and the position of the red car is x = 8.0(20) + 1.5(20)² = 320 meters. Therefore, the red car passes the blue car when they are both at x = 40 meters.
A blue car starts from rest and accelerates at a constant rate of 0.2 m/s² in the positive direction of the x-axis. At t = 2 seconds, a red car traveling in an adjacent lane and in the same direction passes x = 0 with a speed of 8.0 m/s and constant acceleration of 3.0 m/s². Find the time at which the red car passes the blue car.
**Solution**
To solve the problem, we need to determine the position of both cars as a function of time and then find the time at which their positions are equal. We can use the following kinematic equations to determine the position of each car:
- x = x₀ + v₀t + ½at²
where x is the position of the car at time t, x₀ is the initial position, v₀ is the initial velocity, a is the acceleration, and t is the time.
**Calculations for Blue Car**
- Given: x₀ = 0, v₀ = 0, a = 0.2 m/s²
- x = 0 + 0t + ½(0.2)t²
- x = 0.1t²
**Calculations for Red Car**
- Given: x₀ = 0, v₀ = 8.0 m/s, a = 3.0 m/s²
- x = 0 + 8.0t + ½(3.0)t²
- x = 8.0t + 1.5t²
**Finding the Time at which Red Car Passes Blue Car**
To find the time at which the red car passes the blue car, we need to set their positions equal to each other and solve for t.
- 0.1t² = 8.0t + 1.5t²
- 0.4t² - 8.0t = 0
- t(0.4t - 8.0) = 0
This equation has two solutions: t = 0 and t = 20 seconds. The first solution corresponds to the time when both cars are at x = 0, which is not the time when the red car passes the blue car. Therefore, the time at which the red car passes the blue car is:
- t = 20 seconds
**Conclusion**
In conclusion, the red car will pass the blue car after 20 seconds. At this time, the position of the blue car is x = 0.1(20)² = 40 meters, and the position of the red car is x = 8.0(20) + 1.5(20)² = 320 meters. Therefore, the red car passes the blue car when they are both at x = 40 meters.
Community Answer
At t is equal to zero and x is equal to zero and initial stationery bl...
Is it t= 2.05s (appx) ?
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At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car?
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At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car?.
At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At t is equal to zero and x is equal to zero and initial stationery blue car begins to accelerate at the constant rate of 0.2 metre per second square in the positive direction of the x-axis at t is equal to 2 second red car travelling in an adjacent Lane and in the same direction passes x is equal to zero with a speed of 8.0 metre per second and constant acceleration of 3.0 metre per second square at what time will red car passes blue car?.
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