At the start of your vacation, you drive for four hours and 28 minutes, from your home to a cottage you have rented for a week. The car odometer says that the trip covered a distance of 178.7 miles. When you check your GPS, however, it tells you that the straight-line distance from your home to the cottage is 123.3 miles. You might find it helpful to know that there are 1.609344 km in a mile.(a) What is your average speed for your trip from your house to the cottage? Express your answer in units of m/s.__________ m/s(b) What is the magnitude of your average velocity for your trip from your house to the cottage? Express your answer in units of m/s.

Answer:a) 17.88 m/sb) 12.34 m/sStep-by-step explanation:Given:Total time time taken to reach the cottage = 4 hours and 28 minutes or= 4 × 60 + 28 = 268 minutes= 268 × 60 = 16080 seconds Total distance covered = 178.7 milesalso, 1 miles = 1.609344 kmthus, 178.7 miles = 178.7 × 1.609344 km = 287.5897728 Kmalso,1 Km = 1000 m 287.5897728 Km = 287.5897728 × 1000 = 287589.7728 mTotal displacement = 123.3 miles = 123.3 × 1.609344 km = 198432.1152 mNow, a) Speed = [tex]\frac{\textup{Total distance}}{\textup{Total time}}[/tex] orSpeed = [tex]\frac{\textup{287589.7728}}{\textup{16080}}[/tex] orSpeed = 17.88 m/sb) Velocity =  [tex]\frac{\textup{Total displacement }}{\textup{Total time}}[/tex] orVelocity = [tex]\frac{\textup{198432.1152}}{\textup{16080}}[/tex] orVelocity = 12.34 m/s