The numerical value of the vertical velocity of the car at t=0.25 seconds is approximately 0.589m/s.
To determine the vertical velocity of the car at t=0.25 seconds, we can use the expression for vertical velocity in simple harmonic motion. The equation is given by vy =α⋅y0 ⋅cos(ωt), where vy is the vertical velocity, α is the amplitude, y0 is the initial displacement, ω is the angular frequency, and t is time.
Substituting the provided values (y0=0.75m, α=0.95s^−1,ω=6.3s^−1, and t=0.25s) into the equation yields vy =0.95⋅0.75⋅cos(6.3⋅0.25). Evaluating this expression gives a vertical velocity of approximately 0.589m/s at t=0.25 seconds. This represents the speed and direction of the car's vertical motion at that specific time.