Two low-friction carts, A and B

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two low-friction carts, A and B, are on a straight horizontal track. Cart A is at position x=0 mx=0\,\text{m}, while cart B is at x=+30 mx=+30\,\text{m}. The positive xx-axis points to the east. At t=0 st=0\,\text{s} the carts begin moving according to the following schedule of constant velocities: • Cart A: moves eastward at +2.0 m s−1+2.0\,\text{m}\,\text{s}^{-1} for the entire 20 s20\,\text{s} duration considered. • Cart B: moves westward at −1.5 m s−1−1.5\,\text{m}\,\text{s}^{-1} from t=0 st=0\,\text{s} to t=8 st=8\,\text{s}, then instantaneously reverses and moves eastward at +2.5 m s−1+2.5\,\text{m}\,\text{s}^{-1} from t=8 st=8\,\text{s} to t=20 st=20\,\text{s}. Answer all parts fully, showing your reasoning. (a) Write an algebraic expression for the position of each cart as a function of time in its respective time interval. (b) Determine whether the carts ever occupy the same position at the same time in the 00–20 s20\,\text{s} interval. If so, find the meeting time(s) and position(s). If not, explain quantitatively why they never meet. (c) Compute the total distance traveled by cart B during the first 12 s12\,\text{s}. (d) For cart B, calculate (i) the average velocity and (ii) the average speed over the first 12 s12\,\text{s}. Interpret the sign of the average velocity in relation to the track.

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