Use derivatives for velocity and acceleration

Question 1

A particle moves so that its displacement is s = 2t³ + 6t² + 7t metres after t seconds. Find its velocity at t = 3.

Answer 

Question 2

s = 2t³ + 7t (metres, seconds). Find the acceleration at t = 2.

Answer 

Question 3

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

t = 

Question 4

A particle moves so that its displacement is s = 2t³ − 6t² − t metres after t seconds. Find its velocity at t = 2.

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Question 5

s = 2t³ + 3t² + 2t (metres, seconds). Find the acceleration at t = 5.

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Question 6

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

t = 

Question 7

A particle moves so that its displacement is s = t³ + 4t² + 2t metres after t seconds. Find its velocity at t = 3.

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Question 8

s = 2t³ + 10t (metres, seconds). Find the acceleration at t = 2.

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Question 9

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

t = 

Question 10

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

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Question 11

s = 3t³ + 10t (metres, seconds). Find the acceleration at t = 1.

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Question 12

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

t = 

Question 13

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

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Question 14

s = 3t³ + 2t² − 5t (metres, seconds). Find the acceleration at t = 3.

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Question 15

s = t³ − 12t² + 36t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 16

A particle moves so that its displacement is s = 2t³ − 2t² − 4t metres after t seconds. Find its velocity at t = 3.

Answer