The kinematic law of motion of a material point along the Ox axis has the form: x = A + Bt + Ct ^ 2, where A = 5.00 m, B = 10.0 m / s, C = 4.00 m / s2. Determine the projection of the speed of its movement through the time interval Δt = 4.00 s from the beginning of the movement.
x (t) = A + B * t + C * t ^ 2.
A = 5.00 m.
B = 10.0 m / s.
C = 4.00 m / s2.
Δt = 4.00 s
When a body moves with constant acceleration a, the coordinate of the body changes according to the law: x (t) = x0 + V0x * t + ax * Δt ^ 2/2, where x0 is the initial coordinate of the body, V0x is the projection of the initial velocity, and ax is the projection of the acceleration onto coordinate axis.
Therefore, x0 = A = 5.00 m, V0x = B = 10.0 m / s, ax = 2 * C = 2 * 4.00 m / s2 = 8.00 m / s2.
When moving with constant acceleration, the projection of the speed Vx has a dependence: Vx (t) = V0x + ax * Δt.
Vх (t) = 10 + 8 * Δt.
Vх = 10 + 8 * 4 = 42 m / s.
Answer: the body, while moving, increased the projection of the speed to Vx = 42 m / s.
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