Question

Скорость точки движущейся прямолинейно, задана уравнением V=(6t^2-4t-10)м/с. Вычислить её путь за 4 секунды от начала движения

Answer 1

Не знаю, у меня получилось 9 1/3

Answer 2

Calculation of the Path for a Moving Point

To calculate the path of a point moving in a straight line, we need to integrate the given velocity equation over the desired time interval. In this case, the velocity equation is given as V = 6t^2 - 4t - 10 m/s, and we want to find the path for a time interval of 4 seconds from the start of motion.

To calculate the path, we need to integrate the velocity equation with respect to time. The integral of velocity gives us the displacement or path traveled by the point. Let's perform the integration:

∫(6t^2 - 4t - 10) dt

The integral of 6t^2 with respect to t is (2t^3), the integral of -4t with respect to t is (-2t^2), and the integral of -10 with respect to t is (-10t). Integrating each term separately, we get:

(2t^3) - (2t^2) - (10t) + C

where C is the constant of integration.

Now, we can substitute the upper and lower limits of integration to find the displacement or path traveled by the point from the start of motion to 4 seconds. Let's substitute t = 4 and t = 0 into the integrated equation:

Path = [(2 * 4^3) - (2 * 4^2) - (10 * 4)] - [(2 * 0^3) - (2 * 0^2) - (10 * 0)]

Simplifying the equation, we get:

Path = (128 - 32 - 40) - (0 - 0 - 0)

Path = 56 meters

Therefore, the path traveled by the point in 4 seconds from the start of motion is 56 meters.