The driver of a car travelling at 90 mi/h observes a hazard on the road and applies the brakes, giving a constant deceleration of 7.5 ft/s2. If the driver’s reaction time is 0.15 s, how long does it take to stop after sighting the hazard? What distance does the automobile travel before coming to rest?

Question

anonymous · Answer

Consider the following equation:$$v _{f}=v _{i}+at$$where vf is the final velocity; vi is the initial velocity; a is the acceleration; and t is time.  Now if acceleration is negative, i.e. the object in motion is decelerating, you get:$$v _{f}=v _{i}-at$$.  That should help you find the time it takes to decelerate from 90mph to 0mph.

anonymous · Answer

To find the distance traveled while accelerating, we use:$$x=v _{i}t+at ^{2}$$If the acceleration is negative we use:$$x=v _{i}t-at ^{2}$$

anonymous · Answer

Do you see how to solve your problem now?

anonymous · Answer

@PsiSquared  yes, thank you.

anonymous · Answer

You're welcome.