physic-motion in one dimension?

Question

You are driving to the grocery store at 22 m/s. You are 105 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration.
(a) How far are you from the intersection when you begin to apply the brakes?
(b) What acceleration (magnitude) will bring you to rest right at the intersection?
(c) How long (total) does it take you to stop?

Murtaza · Accepted Answer

a) Distance = Speed x Time 
Distance traveled during reaction time = 22 x 0.5 = 11 m

Distance form intersection = 105 - 11 = 94 m

b)
V² = 2as+U²
V will be = 0 m/s

0² = 2(a)(94) + (22)²
a = - 2.574468085 m/s²

Since its ask for magnitude , a = 2.574468085 m/s²

c) 
First let find the time of stopping 
s=½at²ut
94 = 1/2(- 2.574468085)t² + 22t
t = 8.5454545454 s

Total time = 8.5454545454 + 0.5 
= 9.0454545454 s ≈ 9.0 s

JEBalke · Answer

a) 94 m



b) -5.1 m/s2

(vf)^2 = (vi)^2 + a*x
0 = 22^2 + a*94
-484/94 = a

c) 4.8 sec

vf = vi + at
0 = 22 + -5.1t
t = 22/5.1
t = 4.27272727 + .5 (reaction time)


P.S. That's Godly reaction time... average human reaction time is about 1 1/2 seconds

physic-motion in one dimension?

2 Answers