Question

For a given motor vehicle, the maximum achievable deceleration from braking is approximately 8 m/sec2 on dry concrete. On wet asphalt, it is approximately 2.5 m/sec2. Given that 1 mph corresponds to 0.447 m/sec, find the total distance that a car travels in meters on dry concrete after the brakes are applied until it comes to a complete stop if the initial velocity is 67 mph (30 m/sec) or if the initial braking velocity is 56 mph (25 m/sec).

Answer 1

`1.875\ \text{m}`

`1.5625\ \text{m}`

Step-by-step explanation:

`a` = Acceleration on dry concrete =
`-8\ \text{m/s}^2`

`v` = Final velocity = 0

`u` = Initial velocity

`s` = Displacement

For
`u=30\ \text{m/s}`

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0-30)/(2* -8)\\\Rightarrow s=1.875\ \text{m}`

The distance traveled to come to a stop is
`1.875\ \text{m}`

For
`u=25\ \text{m/s}`

`s=(0-25)/(2* -8)\\\Rightarrow s=1.5625\ \text{m}`

The distance traveled to come to a stop is
`1.5625\ \text{m}`.