The altitude of a specialized research probe, $H (t)$ in kilometres, is modelled for time $0.5\,$ seconds using its vertical acceleration.

It is given that:

the acceleration is $12t^2 + \dfrac{2}{t^2}$
the point $P\,$ on the graph of altitude against time has a $t$ -coordinate of 1
the tangent to the graph of $H (t)$ at $P\,$ has the equation $H = 8 t - 3$

Determine the equation of the normal to the graph of altitude against time at the point $P$ . Give your answer in the form $a t + b H + c = 0$ , where $b,\,$ and $c\,$ are integers.

Find an expression for $H (t)$ in terms of $t$ .

The altitude of a specialized research probe, $H (t)$ in kilometres, is modelled for time $0.5\,$ seconds using its vertical acceleration.

It is given that:

the acceleration is $12t^2 + \dfrac{2}{t^2}$
the point $P\,$ on the graph of altitude against time has a $t$ -coordinate of 1
the tangent to the graph of $H (t)$ at $P\,$ has the equation $H = 8 t - 3$

Determine the equation of the normal to the graph of altitude against time at the point $P$ . Give your answer in the form $a t + b H + c = 0$ , where $b,\,$ and $c\,$ are integers.

Find an expression for $H (t)$ in terms of $t$ .

1.8 Integration

Question 51

Markscheme

1.8 Integration

Question 51

Markscheme

1.8 Integration

Question 51

1.8 Integration Questions

1.8 Integration

Question 51

1.8 Integration Questions