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 robot has velocity v(t) = t − 4 m/s for 0 ≤ t ≤ 6. Bo finds the total distance it travels. What is it, in meters?

   10
3. 3.

   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
4. 4.

   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
5. 5.

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

   1.44
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.

   Noah finds the average value of f(x) = eˣ on 0 ≤ x ≤ ln 10. What is it, to the nearest hundredth?

   3.91
8. 8.

   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
9. 9.

   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
10. 10.

    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