Answer to Question #156642 in Classical Mechanics for Eze Nathaniel chizoba

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

Answer 1

Let's first find the velocity of the train for the first 20 seconds:

$$v=v_0+at=0.5\ \dfrac{m}{s^2}\cdot20\ s=10\ \dfrac{m}{s}.$$

The next 30 seconds the train travels with uniform velocity which means that the velocity stays the same - 10 m/s. In further 10 seconds the break are applied and the train comes to rest. Therefore, the velocity of the train becomes zero. Finally we can sketch the velocity time graph of this motion in Excel: