During a trial run a train follows the velocity schedule given below: • From to

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

Problem

During a trial run a train follows the velocity schedule given below: • From t=0 st = 0\,\text{s} to t=12 st = 12\,\text{s}, the velocity rises uniformly from 18 m/s18\,\text{m/s} to 42 m/s42\,\text{m/s}. • From t=12 st = 12\,\text{s} to t=20 st = 20\,\text{s}, the velocity remains constant at 42 m/s42\,\text{m/s}. • From t=20 st = 20\,\text{s} to t=34 st = 34\,\text{s}, the velocity falls uniformly back to 18 m/s18\,\text{m/s}. Answer the following: (a) Calculate the acceleration during the first 12 s12\,\text{s}. (b) Calculate the acceleration during the interval 20–34 s20\text{–}34\,\text{s}. (c) Find the average acceleration of the train over the complete 34 s34\,\text{s} run. (d) Explain why the numerical value obtained in part (iii) has the sign that it does, making reference to the changes in velocity over the entire motion.

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