Use derivatives for velocity and acceleration

Question 1

s = t³ − 9t² + 15t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 2

A particle moves so that its displacement is s = t³ − 5t² − 3t metres after t seconds. Find its velocity at t = 1.

Answer 

Question 3

s = 2t³ − t² + 6t (metres, seconds). Find the acceleration at t = 2.

Answer 

Question 4

s = t³ − 9t² + 24t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 5

A particle moves so that its displacement is s = 3t³ metres after t seconds. Find its velocity at t = 5.

Answer 

Question 6

s = 2t³ + t² + 3t (metres, seconds). Find the acceleration at t = 2.

Answer 

Question 7

s = t³ − 6t² + 9t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 8

A particle moves so that its displacement is s = 3t³ − 2t² + 2t metres after t seconds. Find its velocity at t = 1.

Answer 

Question 9

s = 2t³ − 2t² (metres, seconds). Find the acceleration at t = 2.

Answer 

Question 10

s = t³ − 6t² + 9t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 11

A particle moves so that its displacement is s = 3t³ + t² − 5t metres after t seconds. Find its velocity at t = 4.

Answer 

Question 12

s = t³ − 4t² + 2t (metres, seconds). Find the acceleration at t = 3.

Answer 

Question 13

s = t³ − 9t² + 15t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 14

A particle moves so that its displacement is s = 2t³ + 9t metres after t seconds. Find its velocity at t = 3.

Answer 

Question 15

s = 3t³ − 4t² + 8t (metres, seconds). Find the acceleration at t = 1.

Answer 

Question 16

s = t³ − 12t² + 45t. At what times is the particle at rest? Separate them with a comma.

t =