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

A) The car will hit the barrier

b) 19.82 m/s

Step-by-step 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=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-(75)/(3.6)^2)/(2* -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=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-u^2)/(2* -8.5)\\\Rightarrow s=(u^2)/(17)`

d + s = 35

`\\\Rightarrow u0.6+(u^2)/(17)=35\\\Rightarrow (u^2)/(17)+0.6u-35=0`

`10u^2+102u-5950=0\\\Rightarrow u=(-51+√(62101))/(10),\:u=-(51+√(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.