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A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method?
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A car moving at 30m/s stops with a constant acceleration in a distance...
Given:
Initial velocity, u = 30 m/s
Distance, s = 100 m
Final velocity, v = 0 m/s
To find:
Acceleration, a = ?
Time taken, t = ?
Solution:
We can use the GRESA method to solve this problem. GRESA stands for Given, Required, Equation, Substitution, and Answer.
Given:
u = 30 m/s
s = 100 m
v = 0 m/s
Required:
a = ?
t = ?
Equation:
We can use the equation of motion, which relates the initial velocity, final velocity, acceleration, and distance.
v^2 - u^2 = 2as
Substituting the given values, we get:
0^2 - 30^2 = 2a(100)
-900 = 200a
Simplifying, we get:
a = -4.5 m/s^2
Substitution:
We can use the same equation of motion to find the time taken to stop. We know the initial velocity, final velocity, and acceleration, so we can rearrange the equation to solve for time.
s = ut + (1/2)at^2
Substituting the given values, we get:
100 = 30t + (1/2)(-4.5)t^2
100 = 30t - 2.25t^2
Simplifying, we get a quadratic equation:
2.25t^2 - 30t + 100 = 0
Using the quadratic formula, we get:
t = (30 ± √(30^2 - 4(2.25)(100))) / (2(2.25))
t = (30 ± 24.5) / 4.5
Taking the positive value, we get:
t = 10.2 s
Answer:
The acceleration of the car is -4.5 m/s^2, and the time taken to stop is 10.2 s.
Initial velocity, u = 30 m/s
Distance, s = 100 m
Final velocity, v = 0 m/s
To find:
Acceleration, a = ?
Time taken, t = ?
Solution:
We can use the GRESA method to solve this problem. GRESA stands for Given, Required, Equation, Substitution, and Answer.
Given:
u = 30 m/s
s = 100 m
v = 0 m/s
Required:
a = ?
t = ?
Equation:
We can use the equation of motion, which relates the initial velocity, final velocity, acceleration, and distance.
v^2 - u^2 = 2as
Substituting the given values, we get:
0^2 - 30^2 = 2a(100)
-900 = 200a
Simplifying, we get:
a = -4.5 m/s^2
Substitution:
We can use the same equation of motion to find the time taken to stop. We know the initial velocity, final velocity, and acceleration, so we can rearrange the equation to solve for time.
s = ut + (1/2)at^2
Substituting the given values, we get:
100 = 30t + (1/2)(-4.5)t^2
100 = 30t - 2.25t^2
Simplifying, we get a quadratic equation:
2.25t^2 - 30t + 100 = 0
Using the quadratic formula, we get:
t = (30 ± √(30^2 - 4(2.25)(100))) / (2(2.25))
t = (30 ± 24.5) / 4.5
Taking the positive value, we get:
t = 10.2 s
Answer:
The acceleration of the car is -4.5 m/s^2, and the time taken to stop is 10.2 s.
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A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method?
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A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method?.
A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car moving at 30m/s stops with a constant acceleration in a distance of 100m.calculate the acceleration and rhe time to stop by using GRESA method?.
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