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Prove that v = u + at?
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Prove that v = u + at?
Proving v = u at
Given that the velocity of an object (v) is equal to its initial velocity (u) at a certain time (t), we need to prove that v = u at.
Using the equation of motion
One way to prove this is by using the equation of motion:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Since we are given that v = u at, we can substitute this into the equation:
v = u + a(u/a)
Simplifying this equation, we get:
v = u + u
which gives us:
v = 2u
This equation shows that the final velocity (v) is twice the initial velocity (u). Therefore, the given statement that v = u at is false.
Using the definition of acceleration
Another way to prove this is by using the definition of acceleration:
a = (v - u)/t
where:
- a is the acceleration
- v is the final velocity
- u is the initial velocity
- t is the time
Since we are given that v = u at, we can substitute this into the equation:
a = (u at - u)/t
Simplifying this equation, we get:
a = u(a - 1)/t
This equation shows that the acceleration (a) is equal to the initial velocity (u) multiplied by (a-1)/t. Since the acceleration is not zero, this means that the initial velocity (u) cannot be equal to the final velocity (v) at any time (t). Therefore, the given statement that v = u at is false.
Conclusion
Both methods of proof show that the given statement that v = u at is false. Therefore, it cannot be proven to be true.
Community Answer
Prove that v = u + at?
We know acceleration =v-u/t
a=v-u\t
at=v-u
v-u=at
v=u+at
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Prove that v = u + at?
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Prove that v = u + at? 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 Prove that v = u + at? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that v = u + at?.
Prove that v = u + at? 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 Prove that v = u + at? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that v = u + at?.
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