Final answer:
To find the total distance traveled by Mariah on her bike, you need to calculate the distance covered during each phase of her motion (acceleration, constant speed, and deceleration) and add them together.
Step-by-step explanation:
To find the distance Mariah traveled on her bike, we need to calculate the distance covered during each phase of her motion and then add them together.
First, to find the distance covered during the acceleration phase, we use the formula:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Since Mariah started from rest, her initial velocity is 0 m/s. Given that the acceleration is 3.0 m/s² and the time is 6 seconds, we can calculate the distance covered during acceleration.
Next, during the constant speed phase, we know that the distance covered is equal to the product of the constant speed and the time. The speed remains constant at this stage.
Finally, during the deceleration phase, we use the same formula as for the acceleration phase, but with a negative acceleration value since Mariah is slowing down. Using an acceleration of -5.0 m/s² and a time of 10 seconds, we can calculate the distance covered during deceleration.
Add up the distances from each phase to find the total distance traveled by Mariah on her bike.