You are driving through a town at 12m/s when suddenly a baby rolls out in front of you. You apply the brakes and begin decelerating at 3.5m/s^2. How far do you travel before stopping?
the stopping time (t) is ... 12 m/s / 3.5 m/s^2
d = 1/2 a t^2 + v t = -1.75 t^2 + 12 t
Well, that's quite the unexpected baby sighting! Let's calculate the distance you'd travel before stopping, shall we?
Now, we know your initial velocity is 12 m/s, and you're decelerating at a rate of 3.5 m/s^2. To find the distance, we need to determine how long it takes for you to stop first.
Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can find the time it takes for you to stop.
Since the final velocity (v) is zero when you stop, we have:
0 = 12 m/s + (-3.5 m/s^2)t
Simplifying that equation, we get:
3.5t = 12
Dividing both sides by 3.5, we find t ≈ 3.43 seconds.
Now that we have the time, we can calculate the distance using another equation:
distance = initial velocity × time + 0.5 × acceleration × time^2
Plugging in the values, we get:
distance = 12 m/s × 3.43 s + (0.5 × (-3.5 m/s^2) × (3.43 s)^2
After some math magic, we find that you would travel approximately 58.03 meters before coming to a stop.
So, make sure to keep an eye out for unexpected baby appearances on your travels! Safety first, and maybe pack some baby repellent just in case.
To find out how far you will travel before stopping, we can use the formulas of motion.
The first step is to determine the time it takes for the car to stop. We can find this by using the formula:
v = u + at,
Where:
v = final velocity, which is zero because the car stops
u = initial velocity, which is 12 m/s,
a = acceleration, which is -3.5 m/s^2 (negative because it's in the opposite direction of the car's motion), and
t = time.
Rearranging the formula to solve for t, we have:
t = (v - u) / a.
Substituting the given values, we get:
t = (0 - 12) / -3.5.
Simplifying, we find:
t = 12 / 3.5.
t ≈ 3.43 seconds (rounded to two decimal places).
Now that we know how long it takes for the car to stop, we can determine the distance traveled. We can use the formula:
s = ut + (1/2)at^2,
Where:
s = displacement (distance traveled),
u = initial velocity,
t = time, and
a = acceleration.
Substituting the given values, we get:
s = 12 × 3.43 + (1/2)(-3.5)(3.43)^2.
Simplifying further:
s ≈ 41.16 + (1/2)(-3.5)(11.7649),
s ≈ 41.16 - 20.49492,
s ≈ 20.66508.
Therefore, you will travel approximately 20.67 meters before coming to a stop.