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A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body?
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A body moving with uniform acceleration travels 84m in the first 6seco...
Problem: A body moving with uniform acceleration travels 84m in the first 6 seconds and 180m in the next 5 seconds. Find the initial velocity and acceleration of the body.
Solution:
Step 1: Identify known values
We are given the following values:
- Distance covered in the first 6 seconds (s1) = 84m
- Distance covered in the next 5 seconds (s2) = 180m
- Total time taken (t) = 6 + 5 = 11 seconds
Step 2: Calculate acceleration
We can use the equation: Distance = Initial velocity x time + 1/2 x acceleration x time^2
For the first 6 seconds, we have:
84 = u x 6 + 1/2 x a x (6)^2
Simplifying the equation, we get:
36u + 108a = 84
For the next 5 seconds, we have:
180 = u x 5 + 1/2 x a x (5)^2
Simplifying the equation, we get:
25u + 25a = 36
Solving the above two equations simultaneously, we get:
Initial velocity (u) = 12 m/s
Acceleration (a) = 2 m/s^2
Step 3: Verify the solution
We can verify the solution by using the equations of motion:
v = u + at
s = ut + 1/2 at^2
For the first 6 seconds, we have:
v = 12 + 2 x 6 = 24 m/s
s = 12 x 6 + 1/2 x 2 x (6)^2 = 84 m (matches the given value)
For the next 5 seconds, we have:
v = 24 + 2 x 5 = 34 m/s
s = 24 x 5 + 1/2 x 2 x (5)^2 = 180 m (matches the given value)
Therefore, the initial velocity of the body is 12 m/s and the acceleration is 2 m/s^2.
Solution:
Step 1: Identify known values
We are given the following values:
- Distance covered in the first 6 seconds (s1) = 84m
- Distance covered in the next 5 seconds (s2) = 180m
- Total time taken (t) = 6 + 5 = 11 seconds
Step 2: Calculate acceleration
We can use the equation: Distance = Initial velocity x time + 1/2 x acceleration x time^2
For the first 6 seconds, we have:
84 = u x 6 + 1/2 x a x (6)^2
Simplifying the equation, we get:
36u + 108a = 84
For the next 5 seconds, we have:
180 = u x 5 + 1/2 x a x (5)^2
Simplifying the equation, we get:
25u + 25a = 36
Solving the above two equations simultaneously, we get:
Initial velocity (u) = 12 m/s
Acceleration (a) = 2 m/s^2
Step 3: Verify the solution
We can verify the solution by using the equations of motion:
v = u + at
s = ut + 1/2 at^2
For the first 6 seconds, we have:
v = 12 + 2 x 6 = 24 m/s
s = 12 x 6 + 1/2 x 2 x (6)^2 = 84 m (matches the given value)
For the next 5 seconds, we have:
v = 24 + 2 x 5 = 34 m/s
s = 24 x 5 + 1/2 x 2 x (5)^2 = 180 m (matches the given value)
Therefore, the initial velocity of the body is 12 m/s and the acceleration is 2 m/s^2.
Community Answer
A body moving with uniform acceleration travels 84m in the first 6seco...
Initial velocity= 84/6=14 m/s
Final velocity=180/5= 36m/s
Acceleration=36-14/11-6=22/5 m/s^2
Final velocity=180/5= 36m/s
Acceleration=36-14/11-6=22/5 m/s^2
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A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body?
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A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body?.
A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body moving with uniform acceleration travels 84m in the first 6seconds and 180m in the next 5second. Find the initial velocity and acceleration of body?.
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