The car is initially traveling at a constant speed of 36.7 km/h. To find the distance traveled during the acceleration, we need to determine the final velocity after the acceleration period.
The acceleration is given as 3.0 m/s^2, and the time is 6.2 seconds. We can use the formula: final velocity = initial velocity + acceleration * time)
Converting the initial velocity from km/h to m/s:
Initial velocity = 36.7 km/h * (1000 m/1 km) * (1 h/3600 s) = 10.1944 m/s (rounded to 4 decimal places)
Calculating the final velocity:
Final velocity = 10.1944 m/s + (3.0 m/s^2 * 6.2 s) = 28.8844 m/s (rounded to 4 decimal places)
Now, we can calculate the distance traveled during the acceleration using the formula: distance = (initial velocity * time) + (0.5 * acceleration * time^2)
distance = (10.1944 m/s * 6.2 s) + (0.5 * 3.0 m/s^2 * (6.2 s)^2)
distance = 63.23888 m + 58.548 m
distance = 121.78688 m (rounded to 4 decimal places)
Therefore, the car travels approximately 121.787 meters during the 6.2 seconds of acceleration.