Final answer:
The final velocity of the car after 6.7 seconds, given its initial velocity of 28 m/s due north and an acceleration of 1.4 m/s² north, is 37.38 m/s due north.
Step-by-step explanation:
To find the final velocity of a car after a certain amount of time when given its initial velocity and constant acceleration, we can use the kinematic equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We are given that the car moves with an initial velocity (u) of 28 m/s due north and has a constant acceleration (a) of 1.4 m/s2 also heading north. After 6.7 seconds (t), we want to calculate the final velocity (v) of the car. Plugging these values into the equation:
v = 28 m/s + (1.4 m/s2 × 6.7 s) = 28 m/s + 9.38 m/s = 37.38 m/s due north.
This is the final velocity of the car after 6.7 seconds of acceleration.