Question

A car 3.5 m in length and travelling at a constant velocity of 20 m/s is approaching an intersection. the width of the intersection is 20 m. the light turns yellow when the front of the car is 50 m from the beginning of the intersection. if the driver steps on the brakes the car will slow at -4.2 m/s^2. if the driver instead steps on the gas pedal the car will Excelerator at 1.5 m/s^2. the light will be yellow for three seconds. ignore the reaction time of the driver. to avoid being in the intersection while the light is red, should the driver hit the gas or brake?

Answer 1

Given
t = 3 sec
l = 3.5 m
h = 50 m
d = 20 m
v0 = 20 m/s
a_accel = 1.5 m/s^2
a_brake = - 4.2 m/s^2

Solution

x = x0 + vo * t + a * t^2 / 2


Case 1
Acceleration
Is it true if
x - x0 < vo * t + a_accel * t^2 / 2
l + h + d < vo * t + a_accel * t^2 / 2

3 + 50 + 20 < 20*3+1.5*3^2/2
73 < 66.75
Conclusion The driver have no time to drive


Case 2
Braking
Is it true if
x - x0 > vo * t + a_brake * t^2 / 2
l + h > vo * t + a_brake * t^2 / 2
3 + 50 > 20*3 - 4.2 *3^3/2
53 > 41.1
All ok
Conclusion: the driver must breaking