suppose you are driving at speed V0 when a sudden obstacle in the road forces yo

Question

suppose you are driving at speed V0 when a sudden obstacle in the road forces you to make a quick stop.
a) if your reaction time before the brakes is Tr,what constant declaration (absolute value of ax)do you need to stop in distance d? assume that d is larger than the car travels during your reaction time. Express your answer in terms of the variable V0,d,Tr.
b)suppose you are driving at 28m/s when you suddenly see an abstacle 56m ahead.if your reaction time is 0.50s, what would your cars minimun declaration need to be in order to avoid a collision?
|ax| = ?

Explanation / Answer

a)
Initial speed, vi = Vo
distance = d
Final velovity, vf = 0

distance travelled by car in reaction time = Vo*Tr

So, stopping distance, d' = d - Vo*Tr
use:
vf^2 = vi^2 + 2*a*d'
0 = vo^2 - 2*ax*d'
0 = vo^2 - 2*ax*(d - Vo*Tr)
ax = vo^2 / {2*(d - Vo*Tr)}

b)
use:
ax = vo^2 / {2*(d - Vo*Tr)}
= 28^2 / {2*(56-28*0.5)}
= 9.3 m/s^2

Answer: 9.3 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.