The position of particles moving along x-axis depends on time according to equation x=at2 + bt3 where,x is in meter and t in seconds.What are the unit and dimension of a and b?
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x = at^2 + bt^3
If x is in meters then at^2 and bt^3 should also be in metres.
Hence,
m = a(s)^2
a = m/s^2
Unit of a is m/s^2 and its dimensional formula is [LT^-2]
m = b(s)^3
b = m/s^3
Unit of b is m/s^3 and it’s dimensional formula is [LT^-3]
If x is in meters then at^2 and bt^3 should also be in metres.
Hence,
m = a(s)^2
a = m/s^2
Unit of a is m/s^2 and its dimensional formula is [LT^-2]
m = b(s)^3
b = m/s^3
Unit of b is m/s^3 and it’s dimensional formula is [LT^-3]
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