Question is in description- Please help so confused

Question

Im so confused and need help

 John leadfoot has a reaction time of 1.5 seconds and his car is capable of deceleration at 10m/s2. He is on his way to work when he approaches a pedestrian crossing is 60m away. What is the maximum speed that he can be travelling at and still come to a halt if he sees a child about to cross the road

Answer 1

Use the kinematic relation

 

v_f² - v_i² = 2ad

 

v_f = final speed = 0 (came to a full stop)

 

v_i = initial speed = v = ?

 

d = stopping distance = 60 - 1.5v in meters (initial distance of 60 m reduced by vt = v(1.5) due to reaction time)

 

a = -10 m/s² (negative acceleration)

 

Plug it all into the kinematic relation:

 

0² - v² = 2(-10)(60 - 1.5v)

 

v²  + 30v - 1200 = 0 

 

Solve for v.  Assuming the forward direction is positive, keep the positive solution v = 22.75 m/s.

 

v_max ≅ 22.75 m/s