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A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ?
Most Upvoted Answer
A particle moving with constant acceleration cover a distance of 30m i...
Given Information:
- Distance covered in the 3rd second = 30m
- Distance covered in the 5th second = 50m
Formula:
The distance covered by a particle with constant acceleration can be calculated using the equation:
s = ut + 0.5at²
Where:
s = distance covered
u = initial velocity
t = time
a = acceleration
Using the Formula:
Let's find the acceleration of the particle using the given information.
Distance covered in the 3rd second:
Using the formula, we have:
30 = u(3) + 0.5a(3)²
30 = 3u + 4.5a ---(1)
Distance covered in the 5th second:
Using the formula, we have:
50 = u(5) + 0.5a(5)²
50 = 5u + 12.5a ---(2)
Solving the System of Equations:
To find the values of u and a, we need to solve the system of equations (1) and (2).
Multiplying equation (1) by 2 and equation (2) by 3, we get:
60 = 6u + 9a ---(3)
150 = 15u + 37.5a ---(4)
Subtracting equation (3) from equation (4), we eliminate u:
90 = 9a + 28.5a
90 = 37.5a
Dividing both sides by 37.5, we find:
a = 90 / 37.5
a = 2.4 m/s²
The Acceleration of the Particle:
The acceleration of the particle is 2.4 m/s².
- Distance covered in the 3rd second = 30m
- Distance covered in the 5th second = 50m
Formula:
The distance covered by a particle with constant acceleration can be calculated using the equation:
s = ut + 0.5at²
Where:
s = distance covered
u = initial velocity
t = time
a = acceleration
Using the Formula:
Let's find the acceleration of the particle using the given information.
Distance covered in the 3rd second:
Using the formula, we have:
30 = u(3) + 0.5a(3)²
30 = 3u + 4.5a ---(1)
Distance covered in the 5th second:
Using the formula, we have:
50 = u(5) + 0.5a(5)²
50 = 5u + 12.5a ---(2)
Solving the System of Equations:
To find the values of u and a, we need to solve the system of equations (1) and (2).
Multiplying equation (1) by 2 and equation (2) by 3, we get:
60 = 6u + 9a ---(3)
150 = 15u + 37.5a ---(4)
Subtracting equation (3) from equation (4), we eliminate u:
90 = 9a + 28.5a
90 = 37.5a
Dividing both sides by 37.5, we find:
a = 90 / 37.5
a = 2.4 m/s²
The Acceleration of the Particle:
The acceleration of the particle is 2.4 m/s².
Community Answer
A particle moving with constant acceleration cover a distance of 30m i...
3ms-2
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A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ?
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A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ?.
A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving with constant acceleration cover a distance of 30m in the 3rd second. It covers a distance of 50m in the 5th second. What is the acceleration of the particle ?.
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