Given the data, Jessica jogs a total distance of 15 kilometers (southwards) and then 10 kilometers (northwards), amounting to a total distance of 25 kilometers.
a) To find her speed, we simply need to divide the total distance she ran (25 kilometers) by the time it took (2.5 hours). Thus, speed = Total Distance / Time which results in speed = 25 km / 2.5 hr = 10 km/hr. So, Jessica's speed is 10 kilometres per hour.
b) To find her velocity, we need to take into account the direction Jessica traveled. Velocity is calculated using displacement (total distance in a specific direction) over time. In this case, even though Jessica traveled 25 kilometers in total, her displacement is just 10 kilometers northwards (since she went 15 km south and then came 10 km north, she is 10 km north relative to her starting point). So, velocity = Displacement / Time, which results in velocity = 10 km / 2.5 hr = 4 km/hr. Therefore, Jessica's velocity is 4 kilometers per hour towards the north.