Question

The position of a particle moving along y axis depends on time according to the equation y=at³+bt²,where y is in metre and t is in second.what are the units and dimensions of a and b ? What do they represent physically ?

Answer 1

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Answer 2

Unit of y is metres
Unit of all the terms in that equation should be equal to metres

Therefore,
at³ = m
a (s)³ = m
a = m/s³
Dimension of a = [L T⁻³]

bt² = m
b (s)² = m
b = m/s²
Dimension of b = [L T⁻²]

a represents “j£rk” - Rate of change of acceleration
b represents “acceleration” - Rate of change of velocity.