A car is placed in a wind tunnel and the drag force $F$ for different wind speeds, v, in appropria

Question

A car is placed in a wind tunnel and the drag force $F$ for different wind speeds, v, in appropriate units, is recorded. The results are shown in the table. $v$ $0$ $4$ $8$ $12$ $16$ $20$ $24$ $28$ $32$ $36$ $F$ $0$ $2.5$ $5.1$ $8.8$ $11.2$ $13.6$ $17.6$ $22.0$ $27.8$ $33.9$ Draw the scatter diagram for these values, labeling the axes clearly. It is thought that the drag force $F$ can be modeled by one of the formulae $F=a+bv$ or $F=c+d{{v}^{2}}$ Use your answer to part (i) to explain which of $F=a+bv$ or $F=c+d{{v}^{2}}$ is the better model.

Accepted Answer

(ii) Since the points appear to follow a curve (or trend) that is increasing at an increasing rate (with respect to the variable $v$, the model $F=c+d{{v}^{2}}$ is the better model in this case.

N2010 P2 Q10 [Modified]

N2010 P2 Q10 [Modified]