8. A bus travels 280 km south along a straight path with an average velocity of 80km/h to the south. The bus stops for a 30 minute break, then travels 140 km south with an average velocity of 70km/h to the south. (a) How long does the total trip last? (b) What is the average velocity for the total trip? A car traveling at 7m/s accelerates uniformly at 2.5m/s^2 to reach a speed of 12m/s. How long does it take for the acceleration to occur?

(a) To find the total time for the trip, we need to calculate the time taken for each segment of the journey separately and then add them together.<br /><br />For the first segment, the bus travels 280 km south with an average velocity of 80 km/h. We can use the formula:<br /><br />time = distance / velocity<br /><br />time = 280 km / 80 km/h = 3.5 hours<br /><br />For the second segment, the bus stops for a 30-minute break, and then travels 140 km south with an average velocity of 70 km/h. Again, we can use the formula:<br /><br />time = distance / velocity<br /><br />time = 140 km / 70 km/h = 2 hours<br /><br />The total time for the trip is the sum of the time taken for each segment:<br /><br />total time = 3.5 hours + 2 hours + 0.5 hours = 6 hours<br /><br />Therefore, the total trip lasts for 6 hours.<br /><br />(b) To find the average velocity for the total trip, we need to calculate the total displacement and divide it by the total time.<br /><br />The total displacement is the sum of the displacements for each segment:<br /><br />total displacement = 280 km + 140 km = 420 km<br /><br />The average velocity is given by:<br /><br />average velocity = total displacement / total time<br /><br />average velocity = 420 km / 6 hours = 70 km/h<br /><br />Therefore, the average velocity for the total trip is 70 km/h.<br /><br />(c) To find the time it takes for the acceleration to occur, we can use the formula:<br /><br />time = (final velocity - initial velocity) / acceleration<br /><br />In this case, the initial velocity is 7 m/s, the final velocity is 12 m/s, and the acceleration is 2.5 m/s^2.<br /><br />time = (12 m/s - 7 m/s) / 2.5 m/s^2 = 2 seconds<br /><br />Therefore, it takes 2 seconds for the acceleration to occur.