Final answer:
Without the initial speed and the angle of launch, the vertical velocity of the car at t=0.25 s cannot be determined from the provided values of initial vertical position, vertical acceleration, and angular speed.
Step-by-step explanation:
To evaluate the numerical value of the vertical velocity of a car at time t=0.25 s, we can use the kinematic equations for motion under constant acceleration. The initial velocity in the vertical direction (voy) can be determined by multiplying the initial speed (vo) by the sine of the angle (θ) with respect to the horizontal.
The equation to use, given that the initial vertical position is y0 and the vertical acceleration is α, is y = y0 + voyt + 0.5αt². However, in the absence of the initial speed (vo), the angle (θ), or further context, we cannot provide a specific value for voy at t=0.25 s based solely on the information y0=0.75 m, α=0.951/s, and ω=6.3rad/s.
Additional information regarding initial speed and angle would be required to solve the mathematical problem completely. If these values were provided, the calculation would involve finding voy by multiplying the initial speed with the sine of the angle, and then adjusting for acceleration over time using the kinematic equations.