evaluate the numerical value of the vertical velocity of the car at time t=0.25 s using the expression from part d, where y0=0.75m, α=0.95s^-1, and w=6.3s^-1

The numerical value of the vertical velocity of the car at the given time is 4.91 m/s.

The given parameters;

The final angular velocity of the car at the given time is calculated as;

The numerical value of the vertical velocity of the car at the given time is calculated as;

Thus, the numerical value of the vertical velocity of the car at the given time is 4.91 m/s.

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Given :

Displacement , y = 0.75 m .

Angular acceleration , .

Initial angular velocity , .

To Find :

The value of vertical velocity after time t = 0.25 s .

Solution :

By equation of circular motion is given by :

Putting all given values we get :

Now , vertical velocity is given by :

Therefore , the numerical value of the vertical velocity of the car at time t=0.25 s is 4.90 m/s .

Hence , this is the required solution .