when you see a traffic light turn red you apply the brakes until you come to a stop. if your initial speed was 12 m/s, and you were heading heading due west, what was your average velocity during braking? Assume constant deceleration.
Your average velocity during braking would be 6 m/s due west.
To find the average velocity during braking, we need to determine the time it takes to come to a complete stop. We know the initial speed (v0) is 12 m/s and the final speed (vf) is 0 m/s. We also know that deceleration is the change in velocity per unit time.
Let's assume the time taken to come to a complete stop is t. The equation connecting initial velocity, final velocity, deceleration, and time is:
vf = v0 + at
Since vf is 0 and v0 is 12 m/s, the equation becomes:
0 = 12 + at
Rearranging the equation, we have:
at = -12
The negative sign indicates that the acceleration is in the opposite direction of motion (due west in this case). The average velocity (vav) during braking can be calculated using the following equation:
vav = (v0 + vf) / 2
Since vf is 0, the equation simplifies to:
vav = v0 / 2
Substituting the given value of v0 (12 m/s) into the equation, we get:
vav = 12 / 2
Therefore, the average velocity during braking is:
vav = 6 m/s due west.
To calculate the average velocity during braking, we need to determine the time it takes to come to a complete stop and the distance covered during this time.
Let's break down the problem into steps:
Step 1: Find the time it takes to come to a stop.
To find the time, we need the initial speed and the deceleration. Unfortunately, the deceleration is not given, so we'll assume a constant deceleration value.
Step 2: Find the distance covered during braking.
The distance covered can be calculated using the formula:
distance = initial speed * time + (1/2) * acceleration * time^2
Step 3: Calculate the average velocity using the distance and time.
The average velocity is given by the formula:
average velocity = total displacement / total time
Given that the initial speed is 12 m/s and the car is moving due west, we assume the deceleration value is constant (negative) during braking.
Now let's calculate:
Step 1: Find the time it takes to come to a stop.
Let's assume the deceleration value is -4 m/s².
Using the formula:
final velocity = initial velocity + acceleration * time
0 = 12 - 4 * time
Solving for time:
4 * time = 12
time = 12 / 4
time = 3 seconds
Step 2: Find the distance covered during braking.
Using the formula:
distance = initial speed * time + (1/2) * acceleration * time^2
distance = 12 * 3 + (1/2) * (-4) * 3^2
distance = 36 - 18
distance = 18 meters
Step 3: Calculate the average velocity using the distance and time.
The average velocity is given by the formula:
average velocity = total displacement / total time
Since the car was heading due west and came to a stop, the displacement is equal to the distance covered:
average velocity = 18 meters / 3 seconds
average velocity = 6 meters/second (west)
Therefore, the average velocity during braking is 6 meters/second westward.