Answer to Question #85084 in Physics for Axcel

Question

A race car driver must average 200.0 km/h over the course of a time trial lasting ten laps. If the first 9 laps were done at 199.0km/h, what average speed must be maintained for the last lap?

Answer 1

The average velocity

v_ave=s/t=(s_1+s_2+⋯+s_10)/(t_1+t_2+⋯+t_10 )

Since,

s_1=s_2=⋯s_10=l

t_1=t_2=⋯=t_9=l/v_1

t_10=l/(v_2 )

we obtain

v_ave=10l/(9l/v_1 +l/v_2 )=10/(9/v_1 +1/v_2 )

Or

9/v_1 +1/v_2 =10/v_ave

Finally

v_2=1/(10/v_ave -9/v_1 )=1/(10/200.0-9/199.0)=209.5 km/h