Irodov Problem 1.19

a) the average speed is simply distance covered (half the circumference) over time given by .
b) the average velocity vector is displacement (the diameter) over time given by .
c) If the constant acceleration is w and initially the particle started with 0 speed then,





The final velocity of the particle at the end of the journey will be . This means the average acceleration during this time will be w given by the equation above.

Irodov Problem 1.18

The equations for the curves of various quantities are given below:









If you have solved 1.1-1.17, this needs no explanation.

Irodov Problem 1.17

Let the speed on the highway be v then the speed of the car off the highway is . Let CD = x and let AD=d. The total time taken will be t(AC) + t(BC) given by,






T can be minimized by equating it derivative with respect to x to 0 to obtain the optimal value of x.