The total distance traveled by the car at the given velocity and time is 900 m.
The given parameters:
- initial velocity of the car, u = 20 m/s
- acceleration of the car, a = 12 m/s²
- time of motion of the car, t = 20 s
- final time = 30 s
- final acceleration = 2 m/s²
The final time of motion of car before coming to rest is calculated as follows;
[tex]v_f = v_0 -at\\\\0 = 20 - 2t\\\\t = 10 \ s[/tex]
The graph of the car's motion is in the image uploaded.
The total distance traveled by the car is calculated as follows;
[tex]total \ distance = A \ + B \ + C\\\\total \ distance = (\frac{1 }{2} \times 20 \times 20) \ + (20 \times 30) \ + (\frac{1}{2}\times 10 \times 20)\\\\total \ distance = 900 \ m[/tex]
Thus, the total distance traveled by the car at the given velocity and time is 900 m.
Learn more about velocity-time graph here: https://brainly.com/question/24874645
