Question

a train starts from rest and accelerates uniformly for 30 minutes and attains a velocity of 700 m/s . it then continuous its motion with constant velocity for 2 hours .after then brakes were applied and it comes to rest in 20 minutes ,30 seconds.calculate the total distance travelled by the train during this journey?

Answer 1

Answer on Question #43496, Physics, Mechanics | Kinematics | Dynamics

a train starts from rest and accelerates uniformly for 30 minutes and attains a velocity of 700 m/s. it then continuous its motion with constant velocity for 2 hours. after then brakes were applied and it comes to rest in 20 minutes, 30 seconds. calculate the total distance travelled by the train during this journey?

Solution.

Total distance travelled by the train is the sum of three pieces $L_1$ , $L_2$ and $L_3$ .

For the first segment of motion (uniformly accelerated motion):

$$L _ {1} = V _ {0 1} t _ {1} + \frac {a _ {1} t _ {1} ^ {2}}{2} = \frac {a _ {1} t _ {1} ^ {2}}{2} = \frac {t _ {1} ^ {2}}{2} \left(\frac {V - 0}{t _ {1}}\right) = \frac {V t _ {1}}{2}$$

For the second segment of motion (uniform motion):

$$L _ {2} = V t _ {2}$$

For the third segment of motion (uniformly accelerated motion):

$$L _ {3} = V _ {0 3} t _ {3} - \frac {a _ {3} t _ {3} ^ {2}}{2} = V t _ {3} - \frac {a _ {3} t _ {3} ^ {2}}{2} = V t _ {3} - \frac {t _ {3} ^ {2}}{2} \left(\frac {V - 0}{t _ {3}}\right) = V t _ {3} - \frac {V t _ {3}}{2} = \frac {V t _ {3}}{2}$$

Total distance:

$$L = L _ {1} + L _ {2} + L _ {3} = \frac {V t _ {1}}{2} + V t _ {2} + \frac {V t _ {3}}{2} = V \left(t _ {2} + \frac {t _ {1} + t _ {3}}{2}\right)$$

Numerically:

$$\begin{array}{l} L = 7 0 0 \frac {m}{s} \cdot \left(2 \cdot 6 0 \cdot 6 0 s + \frac {3 0 \cdot 6 0 s + (2 0 \cdot 6 0 + 3 0) s}{2}\right) = 6 1 0 0 5 0 0 m \\ = 6 1 0 0. 5 k m \\ \end{array}$$

Answer: $L = 6100.5 \, \text{km}$

Comment: impossible velocity for the train $700 \, \text{m/s}$ . Check the condition.

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