Average value and motion with integrals

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   A toy cart has velocity v(t) = t − 3 m/s for 0 ≤ t ≤ 5. Ari finds the total distance it travels. What is it, in meters?

   13/2
2. 2.

   A sled has velocity v(t) = t − 5 m/s for 0 ≤ t ≤ 8. Esme finds the total distance it travels. What is it, in meters?

   17
3. 3.

   A toy train has velocity v(t) = t − 3 m/s for 0 ≤ t ≤ 7. Jun finds the total distance it travels. What is it, in meters?

   25/2
4. 4.

   Kira finds the average value of f(x) = eˣ on 0 ≤ x ≤ ln 2. What is it, to the nearest hundredth?

   1.44
5. 5.

   Luz finds the average value of f(x) = eˣ on 0 ≤ x ≤ ln 3. What is it, to the nearest hundredth?

   1.82
6. 6.

   Milo finds the average value of f(x) = eˣ on 0 ≤ x ≤ ln 5. What is it, to the nearest hundredth?

   2.49
7. 7.

   A robot has velocity v(t) = 3t² − 2t m/s. Pia finds its average velocity for 0 ≤ t ≤ 3. What is it, in m/s?

   6
8. 8.

   A sled has velocity v(t) = 3t² − 2t m/s. Ren finds its average velocity for 0 ≤ t ≤ 4. What is it, in m/s?

   12
9. 9.

   A toy train has velocity v(t) = 3t² − 2t m/s. Tala finds its average velocity for 0 ≤ t ≤ 5. What is it, in m/s?

   20
10. 10.

    A toy cart has velocity v(t) = 3t² − 2t m/s. Zee finds its average velocity for 0 ≤ t ≤ 6. What is it, in m/s?

    30