CBSE Class 11-science Answered

A particle is at rest at origin at t =0 it is having a constant acceleration a = (i+j) m/s^2. Position of particle at t=4s is

Asked by arushidabhade | 21 Jul, 2019, 07:54: PM

Expert Answer

acceleration = dv/dt = (i+j) m/s² .......................(1)

where v is velocity in m/s

eqn.(1) is written as, dv = (i+j)dt m/s² ..................(2)

By integrating both sides,

begin mathsize 14px style integral subscript 0 superscript v d v apostrophe space equals space integral subscript 0 superscript t left parenthesis i plus j right parenthesis d t apostrophe space space space w i t h space t h e space c o n d i t i o n space space a t space t apostrophe equals 0 comma space v space equals space 0 w e space g e t comma space v space equals space left parenthesis i plus j right parenthesis space t space space m divided by s sin c e space v e l o c i t y space v space equals space fraction numerator d r over denominator d t end fraction space comma space w e space h a v e space fraction numerator d r over denominator d t end fraction space equals space left parenthesis i plus j right parenthesis space t space space space space space m divided by s............ left parenthesis 3 right parenthesis w h e r e space r space i s space t h e space p o s i t i o n space v e c t o r space f o r space d i s p l a c e m e n t H e n c e space e q n. left parenthesis 3 right parenthesis space i s space w r i t t e n space a s comma space space space d r space equals space left parenthesis i plus j right parenthesis t space d t space space space space space space m space space space....... left parenthesis 4 right parenthesis B y space i n t e g r a t i n g space e q n. left parenthesis 4 right parenthesis comma space integral subscript 0 superscript r d r apostrophe equals space integral subscript 0 superscript t left parenthesis i plus j right parenthesis t apostrophe space d t apostrophe space space space space space comma space w i t h space t h e space c o n d i t i o n space a t space t apostrophe equals 0 space space comma space space space r space equals space 0 space space space w e space g e t comma space space r space space equals space 1 half space t squared open parentheses space i space space plus j space close parentheses space space space space m space space space......... left parenthesis 5 right parenthesis end style

from eqn.(5), we get position of particle at t= 4 , r_t=4 = 8(i+j) m

Answered by Thiyagarajan K | 22 Jul, 2019, 10:39: AM

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CBSE Class 11-science Answered

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