Question

A race car driver must average 200.0 km/h over the course of a time trial lasting ten laps. If the first nine laps were done at an average speed of 196.0 km/h, what average speed must be maintained for the last lap?

Short answer

The obtained average speed of the last lap is ${v_0}^{\prime }\approx 245\mathrm{k}\mathrm{m}/\mathrm{h}$.

Step-by-step solution

Calculation of time

In determining the average speed of the last lap, first, you will need to find out the time taken by the race car driver in the first nine laps and the last lap, respectively.

Now, by using the kinematic equation, you can obtain the average speed.x

Given data:

The average speed of the race car is$v=200\mathrm{k}\mathrm{m}/\mathrm{h}$.

The first nine laps were completed with an average speed of$v_0=196\mathrm{k}\mathrm{m}/\mathrm{h}$.

The relation used to find the time for nine laps is given by:

$t_1=\frac{9L}{v_0}$

The relation used to find the time for the last laps is given by:

$t_2=\frac{1L}{{v_0}^{\prime }}$

Here, ${v_0}^{\prime }$ is the velocity of the last lap.

Calculation of average speed of the last lap

The relation used to find the velocity is given by:

$v=\frac{D}{t_1+t_2}$

Here, D is the total number of laps whose value is 10 L.

On plugging the values in the above relation, you get:

$\begin{array}{r}200\mathrm{k}\mathrm{m}/\mathrm{h}=\left(\frac{10L}{\frac{9L}{196\mathrm{k}\mathrm{m}/\mathrm{h}}+\frac{1L}{{v_0}^{\prime }}}\right)\\ {v_0}^{\prime }=\frac{1}{\frac{10}{200\mathrm{k}\mathrm{m}/\mathrm{h}}-\frac{9}{196\mathrm{k}\mathrm{m}/\mathrm{h}}}\\ {v_0}^{\prime }\approx 245\mathrm{k}\mathrm{m}/\mathrm{h}\end{array}$

Thus, ${v_0}^{\prime }\approx 245\mathrm{k}\mathrm{m}/\mathrm{h}$ is the required average speed of the last lap.