The body moves along the Ox axis with constant acceleration. The projection of the initial velocity of the body

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.