A material point moves in a straight line so that the magnitude of its speed depends

A material point moves in a straight line so that the magnitude of its speed depends on time according to the law U = 4-t (m / s). What is the distance traveled by the point to the stop?

The equation of motion of the body, when moving is equal to accelerated:
v = vo + at
Our expression looks like:
v = 4-1 * t
So vo = 4 m / s, the body moves equally decelerated with an acceleration of -1 m / s². We find the time of movement before stopping from the consideration that v = 0
4-1 * t = 0
t = 4 s.
Find the path traversed by the body from the expression:
S = vot + (a * t²) / 2
Substitute the numerical values:
S = 4 * 4 + (- 1 * 4²) / 2 = 8 m.
Answer: the body will travel 8 m to the stop.



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