Business Smarts - Sample Module for Calculus II

Sample Questions

Calculus II

Motion Problems

Scenario I
A ball is dropped from a height of 250 meters.

1) What is the ball's velocity after 3 seconds of falling?

 a)  -29.4 m/s.

 b)  -9.8 m/s.

 c)  -27.4 m/s.

 d)  29.4 m/s.

 e)  None of the above.

2) What is the ball's position after 3 seconds of falling?

 a)  44.1 m.

 b)  205.9 m.

 c)  -205.9 m.

 d)  -44.1 m.

 e)  None of the above.

3) What distance did the ball travel from t = 0 through t = 3?.

 a)  -205.9 m.

 b)  44.1 m.

 c)  -29.4 m.

 d)  -44.1 m.

 e)  None of the above.

4) What is the ball's velocity after 6 seconds of falling?

 a)  58.8 m/s.

 b)  -58.8 m/s.

 c)  -29.4 m/s.

 d)  -27.4 m/s.

 e)  None of the above.

5) What is the ball's position after 6 seconds of falling?

 a)  176.4 m.

 b)  220.6 m.

 c)  73.6 m.

 d)  -73.6 m.

 e)  None of the above.

6) What distance did the ball travel from t = 3 through t = 6?.

 a)  -132.3 m.

 b)  -44.1 m.

 c)  -176.4 m.

 d)  -220.5 m.

 e)  None of the above.

Scenario II
A ball is thrown down from a height of 500 meters. The ball has a velocity of -16 m/s immediately after its release.

7) What is the ball's velocity t = 4?

 a)  -39.2 m/s.

 b)  55.2 m/s.

 c)  -23.2 m/s.

 d)  -55.2 m/s.

 e)  None of the above.

8) What is the ball's position at t = 4?

 a)  142.4 m.

 b)  485.4 m.

 c)  421.4 m.

 d)  -357.6 m.

 e)  None of the above.

9) What distance did the ball travel from t = 2 through t = 4?.

 a)  -51.6 m.

 b)  -142.4 m.

 c)  -90.8 m.

 d)  -194.0 m.

 e)  None of the above.

10) What is the ball's velocity t = 8?

 a)  -78.4 m/s.

 b)  -16.0 m/s.

 c)  -62.4 m/s.

 d)  -94.4 m/s.

 e)  None of the above.

11) What is the ball's position at t = 8?

 a)  313.6 m.

 b)  414.6 m.

 c)  441.6 m.

 d)  58.4 m.

 e)  None of the above.

12) What distance did the ball travel from t = 6 through t = 8?.

 a)  -169.2 m.

 b)  -272.4 m.

 c)  169.2 m.

 d)  -441.6 m.

 e)  None of the above.

Scenario III
A projectile is launched upward from the ground with a force that gives it an initial velocity of 100 meters per second.

13) What is the projectile's velocity after 5 seconds?

 a)  51.0 m/s.

 b)  -49.0 m/s.

 c)  -51.0 m/s.

 d)  49.0 m/s.

 e)  None of the above.

14) What distance did the projectile travel from t = 2 through t = 5?.

 a)  377.5 m.

 b)  197.1 m.

 c)  180.4 m.

 d)  -197.1 m.

 e)  None of the above.

15) What is the projectile's velocity after 12 seconds?

 a)  -82.4 m/s.

 b)  -117.6 m/s.

 c)  17.6 m/s.

 d)  -17.6 m/s.

 e)  None of the above.

16) What distance did the projectile travel from t = 10 through t = 12?.

 a)  15.6 m.

 b)  -16.4 m.

 c)  -21.2 m.

 d)  -15.6 m.

 e)  None of the above.

Scenario IV
An object that moves along a coordinate line is subject to a force that yields a variable acceleration of a(t) = 6 * t + 4. The object's initial velocity is -38.6 meters per second and an initial position of -125.0 meters.

17) What is the object's velocity at t = 3 seconds?

 a)  39.0 m/s.

 b)  0.4 m/s.

 c)  -0.4 m/s.

 d)  77.6 m/s.

 e)  None of the above.

18) What distance did the object travel from t = 1 through t = 3?.

 a)  -35.6 m.

 b)  -70.8 m.

 c)  -35.2 m.

 d)  35.2 m.

 e)  None of the above.

19) What is the object's velocity at t = 6 seconds?

 a)  -93.4 m/s.

 b)  54.8 m/s.

 c)  132.0 m/s.

 d)  93.4 m/s.

 e)  None of the above.

20) What distance did the object travel from t = 4 through t = 6?.

 a)  114.8 m.

 b)  58.4 m.

 c)  56.4 m.

 d)  2.0 m.

 e)  None of the above.

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