Mathematics 4024 · O Level · Graphs in practical situations

Graphs in practical situations — practice question

For a moving object, its distance, $d$ metres, from an observer after $t$ minutes is given by $d = t^2 + \frac{48}{t} - 20$.
(a)[1]

The table already shows some values of $t$ and $d$. Where appropriate, the $d$ values have been rounded to the nearest whole number. Complete the missing entries.

(b)[2]

Plot the table values on the grid, then connect the points with a smooth curve.

(c(i))[2]

Use a tangent to work out the gradient of the curve when $t = 4$.

(c(ii))[1]

State what this gradient tells you.

(d)[2]

For how long is the object within $10$ metres of the observer?

(e(i))[2]

From your graph, state the two values of $t$ when the object is $12$ metres from the observer. For each one, say whether the object is moving towards or away from the observer.

(e(ii))[1]

Write the equation that gives the values of $t$ when the object is $12$ metres from the observer.

(e(iii))[1]

The equation can be written in the form $t^3 + At + 48 = 0$. Determine $A$.

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