Answer to Question #150378 in Mechanics | Relativity for Abdul Raffih

Question

Kyle is driving his car at 15 m/s when he noticed that he is approaching a stalled truck that is approximately 35m away . He steps on the brakes and the car stops 1.0 m away from the stalled truck . At what rate did the car slow down ? Assume that Kyle's reaction time is 0.20s . Reaction time is the time for a person to notice , think and act in response to a given situation .

Answer 1

Car traectory has 2 parts: 1st - when car moves with constant speed 15m/s during Kyle's reaction time, 2nd - when car moves with constant deleleration till stop. We suppose truck position as zero point and car's beginning position as point -35m

1st part:

$X=X_{o}+\upsilon_{0}\times t$

$X=-35+15\times 0.2=-32m$

2nd part:

$X=X_{0}+\upsilon_{0}\times t+\frac{a\times t^2}{2}$

$X=X_{0}+\upsilon_{0}\times t+\frac{(\upsilon-\upsilon_{0})\times t}{2}$

$-1=-32+15\times t-\frac{15\times t}{2}$

$31=15\times t-7.5\times t$

$31=7.5\times t$

$t=4.13$

$a=\frac{\upsilon-\upsilon_{0}}{t}=\frac{-15}{4.13}=-3.63m/s^2$