How do I solve this physics problem on kinematics?

Question

a driver travelling 25 mi/hr in a school zone can brake an emergency stop in 8.0 ft under similar conditions what would be the breaking distance if the car were travelling 40 mi/hr

Answer 1

I will explain the steps, but YOU do the math.  Use the kinematic relation

 

v² - u² = 2ad

 

v = final speed = 0  [comes to a full stop]

u = initial speed  [given]

a = braking acceleration  [a negative number]

d = stopping distance

 

Assume the braking acceleration is the same at all speeds.  

 

-u² = 2ad

 

a = -u²/(2d)

 

u = 25 mi/hr

d = 8.0 feet

 

I suggest you convert u to ft/s, plug u in ft/s into the equation, plug d = 8.0 feet into the equation, and get a in ft/s².  Then use the result for a to get d for the second question, using u from the second question.

 

-u₁² = 2ad₁

 

d₁ = -u₁²/(2a)

 

Plug in the same braking acceleration a (in ft/s²) from the first question, convert 40 mi/hr to ft/s, plug it in as u₁, and get d₁ in ft.