Question

1. on a drive to cleveland to cincinnati my goal was to average 60 mph for the entire 240-mile trip. my average speed was 50 miles per hour for the first three hours of the trip. what must be my average speed over the rest of the journey if i am to average 60 mph for the entire trip? 3. a train starts from rest and accelerates at a constant rate of 1.0 m/sec² for 30 seconds. after the acceleration period, it stays at a constant

Explanation:

Problem 2:

Step1: Find total time for trip

Total distance = 240 miles, target average speed = 60 mph. Time = Distance / Speed, so total time $t_{total}=\frac{240}{60}=4$ hours.

Step2: Find distance covered in first 3 hours

Speed for first 3 hours = 50 mph, distance $d_1 = 50\times3 = 150$ miles.

Step3: Find remaining distance and time

Remaining distance $d_2 = 240 - 150 = 90$ miles. Remaining time $t_2 = 4 - 3 = 1$ hour.

Step4: Find required average speed for remaining time

Average speed = Distance / Time, so speed $v=\frac{90}{1}=90$ mph.

Step1: Use acceleration formula $v = u + at$

Initial speed $u = 0$ (starts from rest), acceleration $a = 1.0\ m/s^2$, time $t = 30\ s$.

Step2: Calculate final speed

$v = 0 + 1.0\times30 = 30\ m/s$.

Answer:

90 mph

Problem 3: (Assuming we need to find final speed or other, but the question is cut off. If we assume finding final speed after acceleration)