Question

A train starts from a rest from a station and start with uniform acceleration 0.5m/s^2 for 20 seconds. It travels with uniform velocity for 30s. The break are then applied so that a uniform retardation is obtained and the train comes to rest in a further 10 seconds. Sketch the velocity time graphy of this motion. Using your graph calculate the total distance traveled by the train and the total distance traveled using the trapezium method.

Answer 1

Total distance traveled by the train

$$d=d_1+d_2+d_3$$

$$d=\frac{at_1^2 }{2}+vt_2+\frac{v}{2}t_3$$

$$=\frac{0.5\times 20^2}{2}+10\times 30+\frac{10}{2}\times 10=450\:\rm m$$

The total distance also equal to an area on the graph velocity vs time

$$\rm area\: of\: the\: trapezium =\frac{60+30}{2}\times 10=450\: m$$