A particle moves along the x–axis with constant acceleration

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A particle moves along the x–axis with constant acceleration aa. In inertial frame S its motion is described by the kinematic equation x=x0+v0t+12at2.x = x_0 + v_0 t + \tfrac{1}{2} a t^2. A second inertial frame S′ moves with constant velocity uu in the +x–direction relative to S, and the origins of the two frames coincide at t=0t=0. (a) Derive an expression for x′(t)x'(t), the position of the particle as a function of time in frame S′, in terms of x0x_0, v0v_0, aa, uu, and tt. (b) Show explicitly that x′(t)x'(t) can be written in the same functional form x′=x0′+v0′t+12a′t2x' = x'_0 + v'_0 t + \tfrac{1}{2} a' t^2 and identify x0′x'_0, v0′v'_0, and a′a' in terms of the given quantities. (c) Based on your results in part (b), discuss which, if any, of the kinematic parameters depend on the choice of inertial reference frame.

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