CBSE Class 11-science Answered
If acceleration= X². Find velocity when x=2m. Given at x=0 when body is at rest
Asked by shrianshchandra | 12 Apr, 2023, 03:00: AM
Relation between acceleration and displacement is
a = x²
we know,
acceleration,
![a space equals space fraction numerator d v over denominator d t end fraction
a space equals space fraction numerator d v over denominator d x end fraction cross times fraction numerator d x over denominator d t end fraction
a space equals space fraction numerator d v over denominator d x end fraction cross times space v
x squared space equals space v fraction numerator d v over denominator d x end fraction space... left parenthesis f r o m space 1 right parenthesis
x squared d x space equals space v space d v](https://images.topperlearning.com/topper/tinymce/cache/78612c861ef26fd345a766dd13ae3a37.png)
At x = 0 , body is at rest
Thus,
Initial velocity will be 0.
Let velocity at x = 2 be v
∫x²dx = ∫vdv
![integral subscript 0 superscript 2 x squared d x space equals space integral subscript 0 superscript v v space d v
open square brackets x cubed over 3 close square brackets subscript 0 superscript 2 equals open square brackets v squared over 2 close square brackets subscript 0 superscript v
8 over 3 equals v squared over 2
v squared space equals space 16 over 3
v space equals space plus-or-minus 4 divided by square root of 3 space m divided by s](https://images.topperlearning.com/topper/tinymce/cache/d9749f0cb5dbb3046893e7438271a2c9.png)
Answered by Shiwani Sawant | 12 Apr, 2023, 11:04: AM
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