Question

1. Скорость тела изменяется по закону v(t) = 6t^2 - 4t + 1. Какой путь пройдет тело за третью секунду?

Answer 1

A=12
v0=-4
s=-4*3+12*9/2=42m

Answer 2

Calculating the Distance Traveled by the Object

The formula for the velocity of the object is given by v(t) = 6t^2 - 4t + 1. To find the distance traveled by the object in the third second, we can use the formula for distance when the acceleration is constant:

s(t) = v(0)t + (1/2)a(t^2)

where: - s(t) is the distance traveled at time t - v(0) is the initial velocity - a is the acceleration

First, let's find the velocity at the end of the third second, which is v(3): v(3) = 6(3)^2 - 4(3) + 1

Now, we can calculate the distance traveled in the third second using the formula: s(3) = v(0) * 3 + (1/2) * a * (3^2)

Let's calculate the values and find the distance traveled by the object in the third second.

Calculations

- v(3) = 6(3)^2 - 4(3) + 1 - s(3) = v(0) * 3 + (1/2) * a * (3^2)

Results

- v(3) = 6(3)^2 - 4(3) + 1 = 6(9) - 4(3) + 1 = 54 - 12 + 1 = 43 - s(3) = v(0) * 3 + (1/2) * a * (3^2) = 43 * 3 + (1/2) * 6 * (3^2) = 129 + 27 = 156

Therefore, the object will travel 156 units in the third second.