9 Physics Problems and Solutions

1. To qualify for the finals of a racing event, a race car must achieve an average speed of 220 km/h on a track with a total length of 2400 m. If a particular car covers the first 1000 m of the track with an average speed of 180 km/h, what minimum average speed must it have on the remainder of the track to qualify?

3. How long will it take a car, starting from rest and accelerating uniformly at 2.5 m/s2, to travel a distance of 20. m?
(A) 21/2 sec (B) 2.0 sec (C) 4.0 sec (D) 5.0 sec

3. The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

4. A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average apeed for the trip. (b) Determine the distance between the initial and final cities along the route.

5. Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

6. Two cars travel in the same direction along a straight high-way, one at constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15-min lead on the slower car?

7. An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x-direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip, (d) What is her average speed for the round trip?

8. To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 1 600m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event in order to qualify?

9. A certain car is capable of accelerating at a rate of 10.60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 55 mi/h to a speed of 60 mi/h?