Velocity and Acceleration as Functions of Time

HW: Read Sections 2-1 to 2-4, Do QUESTIONS 2 - 4 and 10 and PROBLEMS 5, 8, 9, 13

Questions:
2. Velocity is a vector. An object could travel at constant speed but change direction (as in an object traveling in a circle) which means the velocity changes.

3. No - constant velocity means constant magnitude (speed) and direction.

4. No - if velocity is constant, then the average and instantaneous velocities are equal during that time interval.

10. If down is positive, then an object thrown upwards will have a negative initial velocity with a positive acceleration downwards. By switching up to be the positive direction, the reverse will be true.

Problems:
5. Part I of trip takes (130 mi)/(65 mi/h) = 2 hrs. The trip takes 3 1/3 hours total, so you drive at 55 mi/h for 1 1/3 hours. (55 mi/h)(1 1/3 hrs) = 73.3 miles.
a) total distance = 130 mi + 73.3 miles = 203.3 miles
b) average speed = total distance / total time = (203.3 mi) / (3 1/3 hrs) = 60./9 mi/h

8. average speed = 10.37 m/s, average velocity = 3.46 m/s

9. We have to write position functions for each car. Set x = 0 at train A at t = 0. This makes X_a,o = 0 and X_b,o = 8.5 km.

Train A: X_a = X_a,o + v_a*delta-t
Train B: X_b = X_b,o - v_b*delta-t (negative since train B travels in the opposite direction to Train A.

When the trains meet, their position functions are equal.

Solving, delta-t = .0447 hours or about 2 minutes and 41 seconds.

13. 4.256 m/s²