Problem 58.

You are driving towards a traffic signal when it turns yellow. Your speed is 55 km/h, and your best deceleration has the magnitude of . Your best reaction time before breaking is . To avoid having the front of your car enter the intersection after the light turns red, should you break to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are

(a) 40m and 2.8s, and

(b) 32m and 1.8s?

Solution:

The first step – we need to convert the speed to m/s:

We have two possible types of motion:

1. motion with constant speed till the driver reaches the intersection. Time of this motion is

2. motion with deceleration. The driver starts deceleration after . During this time the driver travels the distance:

The equations which describe these motion are the following:

where the initial position of the car has zero coordinate.

At the final point the velocity is 0. Then

During this time the position of the car is

Now we can analyze the problem:

(a) 40m and 2.8s. Then for motion 1 we have:

Since 2.6<2.8 then the driver can cross the intersection if he will move with constant speed.

(b) 32m and 1.8s. In this case:

Since 2.1>1,8 the driver cannot cross the intersection.

Therefore in this part we need to consider case 2. But even in this case the distance he will travel before he stops is 34.2 m, which is greater than 32 m. Therefore he cannot stop before the intersection.