Course home

9.9 Using Second Derivatives

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 11

The velocity, $v$ $s−1\text{m s}^{-1}$ , of a research drone at time $t$ seconds ( $t > 0$ ) is defined such that its acceleration $a$ follows the equation:

\frac{dv}{dt} = \frac{12}{\sqrt{t}} + \frac{k}{t^3} + 10

where $k$ is a constant.

It is observed that the rate of change of the drone's acceleration is zero at the instant where $t = 4$ .

Determine the value of $k$ .

[4]

Given that the drone's velocity is $100$ $s−1\text{m s}^{-1}$ when $t = 1$ , find an expression for $v$ in terms of $t$ , giving each term in simplest form.

[4]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

9.9 Using Second Derivatives

Question bank

9.9 Using Second Derivatives

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 11

The velocity, $v$ $s−1\text{m s}^{-1}$ , of a research drone at time $t$ seconds ( $t > 0$ ) is defined such that its acceleration $a$ follows the equation:

\frac{dv}{dt} = \frac{12}{\sqrt{t}} + \frac{k}{t^3} + 10

where $k$ is a constant.

It is observed that the rate of change of the drone's acceleration is zero at the instant where $t = 4$ .

Determine the value of $k$ .

[4]

Given that the drone's velocity is $100$ $s−1\text{m s}^{-1}$ when $t = 1$ , find an expression for $v$ in terms of $t$ , giving each term in simplest form.

[4]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.