Question

Поезд движется по закону s=2t ^3+t^2-100t Определить скорость поезда к концу пятой минуты

Answer 1

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Answer 2

Problem Statement

We are given that a train is moving according to the equation of motion s = 2t^3 + t^2 - 100t, where s represents the distance traveled by the train in meters and t represents the time in seconds. We need to determine the velocity of the train at the end of the fifth minute.

Solution

To find the velocity of the train at a specific time, we need to differentiate the equation of motion with respect to time. The derivative of the equation will give us the velocity function.

Let's differentiate the equation s = 2t^3 + t^2 - 100t with respect to t:

ds/dt = d/dt (2t^3 + t^2 - 100t)

To differentiate each term, we can use the power rule:

ds/dt = 6t^2 + 2t - 100

Now we have the velocity function ds/dt = 6t^2 + 2t - 100.

To find the velocity at the end of the fifth minute, we need to substitute t = 5 minutes = 300 seconds into the velocity function.

Let's calculate the velocity:

ds/dt = 6(300)^2 + 2(300) - 100

ds/dt = 540000 + 600 - 100

ds/dt = 540500 m/s

Therefore, the velocity of the train at the end of the fifth minute is 540500 m/s.