Question
A car traveling at the speed of 30.0 m/sec encounters an emergency and comes to a complete stop. how much time will it take for the car to stop if its rate of deceleration is -4.0 m/sec
Answers
Reiny
Using Calculus
a = -4
v = -4t + c
when t=0 , v = 30
30 = 0 + c
v = -4t + 30
s = -2t^2 + 30t + k
when t = 0 , s = 0, so k = 0
s = -2t^2 + 30t
when the car stops, v = 0
4t = 30
t = 30/4 = 7.5 seconds
when t = 7.5
s = -2(7.5)^2 + 30(7.5) = 112.5 m
a = -4
v = -4t + c
when t=0 , v = 30
30 = 0 + c
v = -4t + 30
s = -2t^2 + 30t + k
when t = 0 , s = 0, so k = 0
s = -2t^2 + 30t
when the car stops, v = 0
4t = 30
t = 30/4 = 7.5 seconds
when t = 7.5
s = -2(7.5)^2 + 30(7.5) = 112.5 m