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

Expert Answer

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

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

Answered by Shiwani Sawant | 12 Apr, 2023, 11:04: AM

Concept Videos