1 markDerivative as a Rate of Change (Kinematics and Related Rates)

CSEC Additional Mathematics · 2013 · Paper 2 · Question 8(b)(iii)b)

A particle travels in a straight line such that after t seconds its velocity, v, from a fixed point, O, is given by the function v = 3t² - 18t + 15.

Calculate the value of dv/dt when t = 3 seconds.

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Other parts of this question

8(a)(i)On the graph paper provided, draw a velocity-time graph to illustrate the motion of the particle.[3 marks]
8(a)(ii)a)From your graph determine the total distance, in metres, travelled by the particle.[4 marks]
8(a)(ii)b)From your graph determine the average velocity of the particle for the entire journey.[2 marks]
8(b)(i)Calculate the values of t when the particle is instantaneously at rest.[3 marks]
8(b)(ii)Calculate the distance travelled by the particle between 1 second and 3 seconds.[3 marks]
8(b)(iii)a)Calculate the value of dv/dt when t = 2 seconds.[2 marks]
8(b)(iv)a)Give an interpretation for the value in 8(b)(iii)a).[1 mark]
8(b)(iv)b)Give an interpretation for the value in 8(b)(iii)b).[1 mark]

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