Initial value problems and motion

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   dy/dx = 3x² + 2 and y(1) = 8. Ari finds the particular solution. What is y(2)?

   17
2. 2.

   dy/dx = 6x² − 1 and y(1) = 5. Bo finds the particular solution. What is y(2)?

   18
3. 3.

   dy/dx = 3x² + 4 and y(2) = 1. Esme finds the particular solution. What is y(3)?

   24
4. 4.

   dy/dx = 3eˣ and y(0) = 5. Kira finds the particular solution. What is y(ln 2)?

   8
5. 5.

   dy/dx = 4eˣ and y(0) = -1. Luz finds the particular solution. What is y(ln 2)?

   3
6. 6.

   dy/dx = 5eˣ and y(0) = 9. Noah finds the particular solution. What is y(ln 2)?

   14
7. 7.

   A toy cart has velocity v(t) = 4t + 3 m/s and starts at s(0) = 10 m. Pia finds its position at t = 2. What is s(2), in meters?

   24
8. 8.

   A robot has velocity v(t) = 6t − 5 m/s and starts at s(0) = 2 m. Ren finds its position at t = 3. What is s(3), in meters?

   14
9. 9.

   A sled has velocity v(t) = 2t + 1 m/s and starts at s(0) = -4 m. Tala finds its position at t = 5. What is s(5), in meters?

   26
10. 10.

    A toy train has velocity v(t) = 8t − 3 m/s and starts at s(0) = 6 m. Zee finds its position at t = 2. What is s(2), in meters?

    16