6. Explain whether or not the following particles have an acceleration: (a) a particle moving in a straight line with constant speed, (b) a particle moving around a curve with constant speed.
Ans: (a) no (b) yes. In the second case, the particle is continuously changing the direction of its velocity vector.
7. A sailor drops a wrench from the top of a sailboat’s mast while the boat is moving rapidly and steadily in a straight line. Where will the wrench hit the deck?
Ans: The wrench will hit at the base of the mast. If air resistance is a factor, it will hit slightly leeward of the base of the mast, displaced in the direction in which air is moving relative to the deck. If the boat is scudding before the wind, for example, the wrench’s impact point can be in front of the mast.
8. A particle moves according to the equation x = 10 t2, where x is in meters and t is in seconds. (a) Find the average velocity for the time interval from 2.00 s to 3.00 s. (b) Find the average velocity for the time interval from 2.00 s to 2.10 s.
Ans: (a) 50.0 m/s (b) 41.0 m/s
9. A person walks first at a constant speed of 5.00 m/s along a straight line from point A to poin B and then back along the line from B to A at a constant speed of 3.00 m/s.
(a) What is her average speed over the entire trip?
(b) What is her average velocity over the entire trip?
Ans: (a) 3.75 m/s (b) 0 m/s
10. A hare and a tortoise compete in a race over a course 1.00 km long. The tortoise crawls straight and steadily at its maximum speed of 0.200 m/s towards the finish line. The hare runs at its maximum speed of 8.00 m/s toward goal for 0.800 km and then stops to taunt the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.
Ans: 5.00 m