Question

A train starts from rest and accelerates at 10 m/s2 for 1.5. the train then travels at a constant velocity for 3 minutes. What total distance is coverd by the train in the 4.5 minutes?

Answer 1

A train starts from rest and accelerates at $10\,\mathrm{m/s^2}$ for 1.5. the train then travels at a constant velocity for 3 minutes. What total distance is covered by the train in the 4.5 minutes?

Distance that train covers with acceleration:

$$S_1 = \frac{a t_1^2}{2}$$

Distance that train covers with constant velocity:

$$S_2 = v t_2 = a t_1 t_2$$

Total distance is:

$$S = S_1 + S_2 = \frac{a t_1^2}{2} + a t_1 t_2 = a t_1 \left(\frac{t_1}{2} + t_2\right)$$ $$S = 10\,\mathrm{m/s^2} \cdot 90\,\mathrm{s} \cdot \left(\frac{90\,\mathrm{s}}{2} + 180\,\mathrm{s}\right) = 202500\,\mathrm{m} = 202.5\,\mathrm{km}$$

Answer: $S = 202.5\,\mathrm{km}$