The numerical value of the vertical velocity of the car at the given time is 4.91 m/s.
The given parameters;
- time of motion, t = 0.25 s
- displacement, y₀ = 0.75 m
- angular acceleration, α = 0.95 rad/s²
- angular velocity, ω = 6.3 rad/s
The final angular velocity of the car at the given time is calculated as;
[tex]\omega_f = \omega_o \ + \ \alpha t\\\\\omega_f = 6.3 \ + \ 0.95(0.25)\\\\\omega_f = 6.54 \ rad/s[/tex]
The numerical value of the vertical velocity of the car at the given time is calculated as;
[tex]v= \omega r\\\\v = \omega_f y_o\\\\v = 6.54 \times 0.75 \\\\v = 4.91 \ m/s[/tex]
Thus, the numerical value of the vertical velocity of the car at the given time is 4.91 m/s.
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