Question

A driver of a car going 75 km/h suddenly sees the lights of a barrier 35 m ahead. It takes the driver 0.60 seconds before he applies the brakes, and the average acceleration during braking is -8.5 m/s?. (A) Does the car hit the barrier? (B) What is the maximum speed at which the car could be moving and not hit the barrier 35 meters ahead?

Answer 1

Answer:

A) The car will hit the barrier

b) 19.82 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Distance = Speed × Time

⇒Distance = (75/3.6)×0.6

⇒Distance = 12.5 m

Distance traveled by the car during the reaction time is 12.5 m

Equation of motion

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-\frac{75}{3.6}^2}{2\times -8.5}\\\Rightarrow s=25.53\ m$

Total distance traveled is 12.5+25.53 = 38.03 m

So, the car will hit the barrier

Distance = Speed × Time

⇒d = u0.6

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-u^2}{2\times -8.5}\\\Rightarrow s=\frac{u^2}{17}$

d + s = 35

$\\\Rightarrow u0.6+\frac{u^2}{17}=35\\\Rightarrow \frac{u^2}{17}+0.6u-35=0$

$10u^2+102u-5950=0\\\Rightarrow u=\frac{-51+\sqrt{62101}}{10},\:u=-\frac{51+\sqrt{62101}}{10}\\\Rightarrow u=19.82, -30.02$

Hence, the maximum velocity by which the car could be moving and not hit the barrier 35 meters ahead is 19.82 m/s.