Final answer:
To find where the pickup truck and hatchback car meet up again, use the kinematic equations. Given the truck's constant speed and the hatchback's acceleration, they meet after 3.88 seconds, which corresponds to 110.93 meters traveled by the truck.
Step-by-step explanation:
To determine how far away the pickup truck and hatchback car meet up again, we can use the kinematic equations for constant acceleration. The truck moves at a constant speed of 28.6 m/s, while the hatchback starts from rest and accelerates at 3.8 m/s².
Let's denote the time at which they meet up again as 't'. The position of the truck after time 't' is given by the equation for constant velocity:
Position of truck = velocity × time = 28.6 m/s × t
The position of the hatchback, which starts from rest and accelerates, is given by the equation for constant acceleration:
Position of hatchback = (1/2) × acceleration × (time)² = (1/2) × 3.8 m/s² × t²
Since they meet up at the same position, we can equate the two:
28.6 m/s × t = (1/2) × 3.8 m/s² × t²
Solving for 't' gives us t² = (28.6 m/s) × (2/(3.8 m/s²)) = t² = 15.05263 s², so t = 3.88 s (rounded to two decimal places).
Finally, plugging 't' back into one of our position equations (either truck or hatchback, since they are at the same location) will give us the distance where they meet:
Position = 28.6 m/s × 3.88 s = 110.93 m (rounded to two decimal places)