Question

S=4+3t-0,5^2(м) через сколько секунд после начала движения тело остановится?

Answer 1

Через три секунды.

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Answer 2

To find when the body comes to a stop, we need to find the value of t when the velocity (v) of the body is zero. The given equation represents the velocity of the body at time t:

v(t) = 4 + 3t - 0.5t^2

When the body stops, its velocity (v) will be zero. So, we can set v(t) equal to zero and solve for t:

0 = 4 + 3t - 0.5t^2

To solve this quadratic equation, we can rearrange it into standard form:

0.5t^2 - 3t - 4 = 0

Now, we can use the quadratic formula to find the values of t:

The quadratic formula is: t = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 0.5, b = -3, and c = -4.

t = [ -(-3) ± √((-3)^2 - 4 * 0.5 * (-4)) ] / (2 * 0.5) t = (3 ± √(9 + 8)) / 1 t = (3 ± √17) / 1

Now, we get two possible values for t:

1. t = (3 + √17) ≈ 5.12 seconds (approximately)
2. t = (3 - √17) ≈ -1.12 seconds (approximately)

Since time cannot be negative in this context, we discard the second solution. Therefore, the body will stop approximately 5.12 seconds after the start of its motion.