Question

A driver is traveling 18.0 m/s when she sees a red light ahead. Her car is capable of decelerating at a rate of 3.65 m/s2. If it takes her 0.350 s to get the brakes on and she is 20.0 m from the intersection when she sees the light, will she be able to stop in time? How far from the beginning of the intersection will she be, and in what direction?

Answer 1

The driver will be able to stop in time. The car will come to a stop approximately 6.0 meters from the beginning of the intersection.

Step-by-step explanation:

To determine if the driver will be able to stop in time, we need to calculate the distance the car will travel during the deceleration period. We can use the equation:

d = vi*t + 0.5*a*t^2

where d is the distance, vi is the initial velocity, t is the time, and a is the acceleration (deceleration in this case).

Plug in the given values:

vi = 18.0 m/s

a = -3.65 m/s^2 (negative sign indicates deceleration)

t = 0.350 s

Using the equation, we can find the distance:

d = (18.0 m/s)(0.350 s) + 0.5(-3.65 m/s^2)(0.350 s)^2

d = 6.3 m + 0.5(-3.65 m/s^2)(0.1225 s^2)

d = 6.3 m - 0.315 m

d = 5.985 m ≈ 6.0 m

Therefore, the car will be able to stop in time, as the distance is less than 20.0 m. The car will come to a stop approximately 6.0 meters from the beginning of the intersection.

The direction of the car's movement will be the same as before, as it is only decelerating and not changing direction.

Answer 2

We use equation of motion,

`v^(2) = u^(2) +2 as`.

Here, v is final velocity of the body, u is initial velocity of the body, a is acceleration of the body and s is distance covered by body.

She travels a distance = 18 x 0.350 = 6.3 m.

Therefore, she is [20 - 6.3] = 13.7 m from the intersection.

As her car is capable of decelerating at a rate of 3.65 m/s2

So,

`0 = (18 .0 m/s)^2 -2 * (3.65 \ m/s^2) s \\\\ s = ((18 m/s)^2 )/((2 *3.65 m/s^2) ) = 44 .38 \ m`.

She does not get stopped before the intersection.

Thus, she is 44.38-13.7 = 30.7 m ahead of the intersection.