The body moves along the Ox axis with constant acceleration. The projection of the initial velocity of the body is vor = 5.0 m / s, the projection of the acceleration is ax = -3.0 m / s2. What is the projection of the body’s velocity by the moment when the projection of displacement is Δrx = -24m?
According to the condition, the movement is uniformly slowed down. This means that the moment of time t, when the projection of the displacement becomes equal to -24 m, we find from the equation:
-24 = 5t – 3t ^ 2/2, or
1.5t ^ 2 – 5t – 24 = 0,
D = (-5) 2 – 4 * 1.5 * (- 24) = 169,
The root of D = 13, and
t = (5 + 13) / (2 * 1.5) = 6 s or t = (5 – 13) / (2 * 1.5) = -2.67 s.
The conditions correspond to t = 6 s> 0.
Desired speed projection
vx = v0x + at = 5 – 3 * 6 = -13 m / s.
The projection is negative, that is, the direction of the velocity at the moment t = 6 s is opposite to the direction of the Ox axis.
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