a person is driving unsafely on the highway at a speed of 145km/h and has to slam on the brakes in order to avoid collision. the brakes can slow down the car at a rate of 10.4m/s^2. how far will the car travel while slowing down?
idk
To calculate the distance the car will travel while slowing down, we need to determine the time it takes for the car to come to a stop using the given deceleration rate.
First, we need to convert the car's speed from km/h to m/s:
145 km/h = 145,000 m/ (60 × 60) s = 40.28 m/s
We can use the formula:
acceleration = (final velocity - initial velocity) / time
Since the car is coming to a stop, the final velocity is 0 m/s and the initial velocity is 40.28 m/s. The deceleration rate is given as -10.4 m/s^2.
-10.4 m/s^2 = (0 m/s - 40.28 m/s) / time
Solving for time:
-10.4 m/s^2 × time = -40.28 m/s
time = -40.28 m/s / -10.4 m/s^2
time ≈ 3.88 seconds
Now, we can use the formula:
distance = initial velocity × time + (0.5 × acceleration × time^2)
distance = 40.28 m/s × 3.88 s + (0.5 × -10.4 m/s^2 × (3.88 s)^2)
distance ≈ 156.53 m
Therefore, the car will travel approximately 156.53 meters while slowing down.
To find the distance the car will travel while slowing down, we can use the formula:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car comes to a stop)
u = initial velocity (145 km/h or 145,000 m/3600 s, converted to m/s)
a = acceleration (-10.4 m/s^2, since the brakes are slowing down the car)
s = distance traveled
Step 1: Convert the initial velocity from km/h to m/s:
u = 145,000 m/3600 s = 40.28 m/s
Step 2: Plug the values into the formula:
0^2 = (40.28)^2 + 2(-10.4)s
Step 3: Calculate:
0 = 1622.98 - 20.8s
Step 4: Rearrange the equation to solve for distance, s:
20.8s = 1622.98
s = 1622.98 / 20.8
s ≈ 78.13 m
Therefore, the car will travel approximately 78.13 meters while slowing down.
To determine the distance the car will travel while slowing down, we can use a physics equation known as the kinematic equation:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity
vi = initial velocity
a = acceleration
d = distance
Given:
vi = 145 km/h = 145000 m/3600 s ≈ 40.279 m/s (converted to meters per second)
a = -10.4 m/s^2 (negative because the car is decelerating)
We need to find the distance traveled (d) while slowing down the car, so we rearrange the equation:
d = (vf^2 - vi^2) / (2a)
As the car comes to a stop while decelerating, the final velocity (vf) will be zero. Substituting the values into the equation:
d = (0 - 40.279^2) / (2 * -10.4)
d = (-1628.243441) / (-20.8)
d ≈ 78.275 meters
Therefore, the car will travel approximately 78.275 meters while slowing down.