Question

Suppose you have a car with a maximum acceleration of a=6.0m/s^2 and a maximum deceleration from braking of a=-8.0m/s^2.we want to find the minimum time it would take you to start from rest , cover 500m, and come to a stop at the 500m mark, you do this by accelerating as much as possible for a part of the 500m m, followed by a period of maximum deceleration to the final stop,.find the minimum time

Answer 1

Answer:

time = 17.08 sec.

Explanation:

Given, a₁=6 m/sec , a₂ = -8 m/sec

Let v be the max speed attained

using v² - u² = 2as

v² - 0 = 2a₁s₁                                  0² - v² = 2a²₂s₂

s₁= v²/2a₁                                         s₂= -v²/2a₂

500 = s₁ + s₂

       = v²/12 + v²/16

v = 58.55 m/sec

t = t₁ + t₂ = v/a₁ - v/a₂

 = v(1/6 + 1/8)

 =58.55 × 7/24

t = 17.1 sec.