- Mathematical Problems
- (I) During a canoe race, a camper paddles 353 m in the first 50.0 s then paddles an additional 53 m in 20.0 s. What is the average speed in m/s and km/h?
- (I) A rocket launched into outer space travels 2.4 x 105 km during the first 6.0 hours after launching. What is the average speed of the rocket in m/s?
- (I) An electron takes 1.6 x 10-3 s to travel through a vacuum tube at a constant speed of 1300 m/s. What is the length of the vacuum tube?
- (II) Light from the sun reaches the earth in 8.3 minutes. The speed of light is 3.0 x 108 m/s. In kilometers, how far is the earth from the sun?
- (I) What is the acceleration of a racing car if its speed is decreased from 66 m/s to 44 m/s over an 11 s period?
- (I) How long does it take a train moving at a speed of 15 m/s to accelerate uniformly to 45 m/s at a rate of 2.5 m/s2?
- A car starts from rest and accelerates at a constant rate a reaching a velocity of v at the end of a time period t. Which of the following statements are true?
- The acceleration a must be greater than the final velocity v.
- The average velocity of the car during t is EXACTLY v/2.
- The average velocity of the car during t is GREATER than v/2.
- The final velocity of the car v will be EXACTLY a times t.
- I only
- IV only
- III only
- II and IV
- I, II, and IV
- (I) A bullet leaves the muzzle of a rifle in a direction straight up with a speed of 700 m/s. Ten (10.0) seconds later, its speed is only 602 m/s. At what rate does the earth’s gravitational field slow the bullet?
- (II) A car traveling at 44 m/s is uniformly accelerated to a speed of 22 m/s over an 11 s period. What distance does the car travel during this time?
- (II) A rocket traveling at 88 m/s is accelerated to 132 m/s. How long does it take to travel 660 m?
- (II) An engineer is designing a runway to accommodate airplanes that must gain a ground speed of 60.0 m/s before they can take off. If the planes are capable of being accelerated at 1.5 m/s2, how much time will be required for the planes to reach 60.0 m/s? How long must the runway be?
- (II) The Tokyo Express is accelerated from rest for 1.0 minute while traveling 1800 m. At what rate did it accelerate?
- (II) A box falls off of a tailgate and slides along the street for a distance of 62.5 m. Friction slows the box at –5.0 m/s2. At what speed was the truck traveling when the box fell?
- (II) A wrench falls from a helicopter rising at a constant speed of 6.0 m/s.
- After 2 s, what is the velocity of the wrench?
- After 2 s, how far below the helicopter is the wrench?
- (III) A driver going 90 km/h suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s before he applies the brakes and the average acceleration during braking is -10.0 m/s2.
- Does the car hit the barrier?
- How fast could the car be moving and not hit the barrier?
- (II) An arrow is shot straight up from a height of 1.50 m with an initial speed of 45 m/s.
- How long before the arrow reaches its maximum height?
- What is the maximum height the arrow reaches?
- What is the velocity of the arrow when it returns to the point where it was launched?
- How long after launch before the arrow returns to its original height?
1)5.80 m/s; 20.9 km/h / 2)11,000 m/s / 3)2.1 m / 4)1.5 x 108 km
5)-2.00 m/s2 / 6)12 m/s / 7)d / 8)-9.8 m/s2
9)360 m / 10)6.00 s / 11)40 s; 1200 m / 12)1.0 m/s2
13)25 m/s / 14)a. -14 m/s b. 20 m below / 15)a. yes b. 22 m/s
16)a. 4.59 s b. 103 m
c. -45.0 m/s d. 9.18 s / 17) / 18)
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