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Grade 11Mechanics

The position of a particle moving along the x axis depends on the time according to the equation x=at2+bt2 where x is in meter and t is in sec what are the units and dimensions of a and b? What do they represent?

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Profile image of Simran
9 Years agoGrade 11
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1 Answer

Profile image of Amrit Raj
9 Years ago
Here ,it is given that
x=at2+bt3
Since on LHS,  x is in meter. So on the RHS at2  AND bt3 should also be in meters individually.
Now using dimentional anlysis ,
at2=L
=>aT2=L
=>a=LT(-2) 
which means unit of a is m/s2  ,thus a represent acceleration(rate of change of velocity) and dimention is MoLT(-2) .
bt3=L
=>bT3=L
=>b=LT(-3) 
which means unit of a is m/s3  ,thus a represent jerk (rate of change of  acceleration) and dimention is MoLT(-3) .