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 $k$ .

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.

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 $k$ .

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.

1.6 Differentiation

Question 25

Markscheme

1.6 Differentiation

Question 25

Markscheme

1.6 Differentiation

Question 25

1.6 Differentiation Questions

1.6 Differentiation

Question 25

1.6 Differentiation Questions