Question

The problem is: You apply your brakes to stop for a traffic light, and you come to a stop in a distance of 35 meters. How much time did it take you to stop?

from previous problems, i know:

INITIAL VELOCITY: 15 m/s
FINAL VELOCITY: 0 m/s
ACCELERATION: -3 m/s^2 (because you're slowing down)
DISPLACEMENT: 35 m

so we're solving for time.

i used the displacement= (initial velocity x delta t) + 1/2 (a)(delta t)^2 and got 3.7 seconds (used quadratic formula).


35= 15 (delta t) + 1/2 (-3) (delta t)^2

then put that into the quadratic formula.

[-15 +/- root 225-(4)(-1.5)(-35)]/-3

then (-15 +/- 3.87) / -3.

however, according to the answer sheet, the answer should be 4.7 seconds, not 3.7.. what did i do wrong?

Answer 1

INITIAL VELOCITY, v0: 15 m/s
FINAL VELOCITY, v1: 0 m/s
ACCELERATION, a: -3 m/s^2 (because you're slowing down)
DISPLACEMENT, S: 35 m
These numbers do not work.
The equation is supposed to be:
v1²-v0²=2aS
0-15² = 2*(-3)(35)
225 = 210
Something is amiss.

Correct either the acceleration or v0 will probably solve the problem.