$4.$ Supposee that a racecar driver is testing a car on a racetrack and his team is monitoring the car's speed at two points $\backslash ($ P $\backslash )$ and $\backslash ($ Q $\backslash )$ on the road. Point $\backslash ($ P $\backslash )$ is in the middle of a straight section of the track, while point $\backslash ($ Q $\backslash )$ is on a curved portion of the track. The team records the following information concerning two different laps around the track. First Lap $-$ speed at $\backslash ($ P$=160\backslash$mathrm$\{$mph$\}\backslash ),$ speed increasing at $\backslash ($ P $\backslash )$ at rate of $\backslash (10\backslash$mathrm$\{$mph$\}/\backslash$mathrm$\{$sec$\}\backslash )-$ speed at $\backslash ($ Q$=100\backslash$mathrm$\{$mph$\}\backslash ),$ speed decreasing at $\backslash ($ Q $\backslash )$ at rate of $\backslash (5\backslash$mathrm$\{$mph$\}/\backslash$mathrm$\{$sec$\}\backslash )$ Second Lap $-$ speed at $\backslash ($ P$=200\backslash$mathrm$\{$mph$\}\backslash ),$ speed increasing at $\backslash ($ P $\backslash )$ at rate of $\backslash (5\backslash$mathrm$\{$mph$\}/\backslash$mathrm$\{$sec$\}\backslash )-$ speed at $\backslash ($ Q$=50\backslash$mathrm$\{$mph$\}\backslash ),$ speed increasing at $\backslash ($ Q $\backslash )$ at rate of $\backslash (8\backslash$mathrm$\{$mph$\}/\backslash$mathrm$\{$sec$\}\backslash )($i$)$ Going from the first lap to the second lap, did the absolute value of the tangential component of acceleration at point $\backslash ($ P $\backslash )$ increase, decrease, or stay the same. If it changed, what was the percent change? $($ii$)$ Going from the first lap to the second lap, did the normal component of acceleration at point $\backslash ($ P $\backslash )$ increase, decrease, or stay the same. If it changed, what was the percent change? $($iii$)$ Going from the first lap to the second lap, did the absolute value of the tangential component of acceleration at point $\backslash ($ Q $\backslash )$ increase, decrease, or stay the same. If it changed, what was the percent change? $($iv$)$ Going from the first lap to the second lap, did the normal component of acceleration at point $\backslash ($ P $\backslash )$ increase, decrease, or stay the same. If it changed, what was the percent change? $($v$)$ Deteremine the value $\backslash (\backslash$kappa $\backslash )$ of the curvature at point $\backslash ($ Q $\backslash )$ such that $\backslash (\backslash |\backslash$vec$\{$a$\}\backslash |\backslash )$ is unchanged going from the first lap to the second lap.