Question

the velocity of a particle v at an instant t is given by v =at+bt2. the dimensions of b is

Answer 1

Velocity = at + bt²

Differentiating both the sides w.r.t. time,

dv/dt = d(at + bt²)/dt

⇒ $\vec{a}$ = a + 2bt

From the Principles of the Homogeneity of the Dimensions, dimensions in each and every terms remains same.

∴ Dimension of the Acceleration will be same as a and bt.

Dimensions of the Acceleration = LT⁻²

∴ [b][T] = LT⁻²

⇒ [b] = LT⁻³

Hence, the dimensions of the b is LT⁻³.

Hope it helps. :-)

Answer 2

Answer:

dimensions of B is LT^-3