The speed-time curve for a local train is shown in figure below. In this time, AB represents

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PTCUL AE E&M 2017 Official Paper (Set B)

Option 1 : Coasting

__Speed - Time curve:__

The curve drawn between speed and time is called the speed-time curve. It gives complete information about the motion of the train. The curve gives the speed at various instants after the start of the run directly. The slope of the curve at any point gives the acceleration at the corresponding instant or speed.

Quadrilateral speed - time curve:

- The quadrilateral speed time curve is a close approximation to the urban and suburban services where short distances are involved.
- The assumption for the quadrilateral speed time curve is the initial acceleration and coasting retardation periods extended.
- And there is no free-running period.

The quadrilateral speed time curve is shown in the below figure,

The quadrilateral speed time curve consists of three periods namely acceleration, coasting, and braking periods.

Acceleration:

In the curve, shown above the period up to T1 is actually the Acceleration period. In this period the voltage will be constant, and the current will be decreasing and become constant, tractive effort is equal to resistance to the motion of the train. And in the acceleration period the slope of the curve is positive, hence the acceleration during this period is positive.

Coasting:

The period between the instants T1 and T2 is called the Coasting period. In this period the power supply is cut off and the train is allowed to run under its own momentum. The speed of the train starts decreasing on the account of resistance to the motion of the train. The rate of decrease in speed during this period is known as coasting retardation. In the coasting period, the slope of the curve is negative, hence the acceleration during this period is negative.

Retardation or breaking period:

At the end of the coasting period brakes are applied to bring the train to rest. During this period speed decreases rapidly and finally reduced to zero. In this Retardation period also the slope of the curve is negative, so the acceleration during this period also negative.

Note:

Hence, in the quadrilateral speed time curve, the acceleration during successive periods is positive, negative, and negative respectively.

__Important Points__

- The trapezoidal speed time curve can be approximated from the actual speed time curve by assuming acceleration and retardation kept the same as the actual speed-time curve and running and coasting periods are replaced by a free-running period or constant speed.
- In the free-running period, the speed of the train is constant or the slope of the curve is zero, hence the acceleration during this period is zero.
- During the successive period of the trapezoidal speed-time curve the accelerations are positive, zero, and negative respectively.