Position, velocity, speed and acceleration

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   A toy cart is at s(t) = t³ − 9t² + 15t meters for t > 0. Ari finds when it is speeding up. Which is right?

   • 1 < t < 3 or t > 5
   • 1 < t < 5
   • t > 3
   • t > 5
2. 2.

   A robot is at s(t) = t³ − 9t² + 24t meters for t > 0. Bo finds when it is speeding up. Which is right?

   • 2 < t < 4
   • t > 4
   • t > 3
   • 2 < t < 3 or t > 4
3. 3.

   A toy train is at s(t) = t³ − 6t² + 9t meters for t > 0. Esme finds when it is speeding up. Which is right?

   • t > 3
   • t > 2
   • 1 < t < 3
   • 1 < t < 2 or t > 3
4. 4.

   A sled on a track is at s(t) = t³ − 12t² + 36t meters for t > 0. Jun finds when it is speeding up. Which is right?

   • 2 < t < 6
   • t > 6
   • 2 < t < 4 or t > 6
   • t > 4
5. 5.

   A sled on a track is at s(t) = t³ − 9t² + 15t meters. It stops twice. Kira finds its acceleration at the second stop. What is it, in m/s²?

   12
6. 6.

   A robot is at s(t) = t³ − 12t² + 21t meters. It stops twice. Milo finds its acceleration at the second stop. What is it, in m/s²?

   18
7. 7.

   A toy train is at s(t) = 2t³ − 15t² + 24t meters. Pia finds its speed at t = 2. What is it, in m/s?

   12
8. 8.

   A sled on a track is at s(t) = 2t³ − 15t² + 20t meters. Ren finds its speed at t = 3. What is it, in m/s?

   16
9. 9.

   A toy cart is at s(t) = 2t³ − 15t² + 10t meters. Tala finds its speed at t = 1. What is it, in m/s?

   14
10. 10.

    A robot is at s(t) = 2t³ − 15t² + 14t meters. Zee finds its speed at t = 4. What is it, in m/s?

    10