A car is traveling at a speed of 80 km/h when the brakes are suddenly applied, causing a constant deceleration of 3.24 m/s2. Determine the time required to stop the car and the distance traveled before stopping
Vi = 80,000 m/3600 s
a = -3.24
v = Vi + a t
0 = 80/3.6 - 3.24 t
d = Vi t + (1/2) a t^2
= (80/3.6) t - 1.62 t^2
Oh, dear car, why did you get yourself into this situation? Now let's see how long it will take for you to come to a full stop and how far you'll go before that.
We know that the car's initial speed is 80 km/h. Let's convert that to m/s because we love consistent units. So, 80 km/h is equal to 22.2 m/s. Got it?
Now, let's calculate the time it takes for the car to stop. We know that deceleration is a negative acceleration, so -3.24 m/s² it is. Using the formula 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 substitute the values.
0 (final velocity) = 22.2 (initial velocity) + (-3.24) (acceleration) × t (time)
Solving for t, we get:
0 = 22.2 - 3.24t
Rearranging the equation:
3.24t = 22.2
t = 22.2 / 3.24
t ≈ 6.85 seconds.
So, it will take approximately 6.85 seconds for the car to come to a complete stop. Hang in there, car!
Now, let's calculate the distance traveled before stopping. We can use the formula s = ut + 0.5at², where s is the distance traveled.
s = 22.2 (initial velocity) × 6.85 (time) + 0.5 (-3.24) (acceleration) × (6.85)²
s = 152.07 - 68.20
s ≈ 83.87 meters.
Therefore, the car will travel approximately 83.87 meters before coming to a halt. And that, my friend, is why we always need to be careful when applying the brakes. Stay safe out there!
To determine the time required to stop the car and the distance traveled before stopping, we can use the equations of motion.
Step 1: Convert the speed of the car from km/h to m/s.
Given: Initial speed (u) = 80 km/h
To convert from km/h to m/s, we need to multiply by a conversion factor of 1000/3600.
80 km/h = (80 * 1000) / 3600 = 22.22 m/s (approximately)
Step 2: Determine the final speed (v) when the car comes to a stop.
The final speed of a car when it comes to a stop is 0 m/s.
Step 3: Use the formula of motion v^2 = u^2 + 2as to find the distance traveled (s) before stopping.
Given: Acceleration (a) = -3.24 m/s^2 (negative sign indicates deceleration)
Final speed (v) = 0 m/s
Initial speed (u) = 22.22 m/s
Distance traveled (s) = ?
Rearranging the formula, we get:
s = (v^2 - u^2) / (2a)
Substituting the values:
s = (0^2 - 22.22^2) / (2*(-3.24))
= (-492.8388) / (-6.48)
= 76.0148 meters (approximately)
Step 4: Calculate the time required (t) to stop.
We can use the formula of motion v = u + at, where v = 0 m/s, u = 22.22 m/s, and a = -3.24 m/s^2.
v = u + at
0 = 22.22 + (-3.24)t
Rearranging the formula, we get:
t = (v - u) / (-a)
Substituting the values:
t = (0 - 22.22) / (-(-3.24))
= 22.22 / 3.24
≈ 6.8457 seconds (approximately)
Therefore, the time required to stop the car is approximately 6.8457 seconds, and the distance traveled before stopping is approximately 76.0148 meters.
To find the time required to stop the car and the distance traveled before stopping, we can use the equations of motion.
The first equation we will use is the equation of motion to find the time (t) required to stop the car:
vf = vi + at
Where:
vf = final velocity (which is 0 since the car stops)
vi = initial velocity of the car (80 km/h = 80 * (1000/3600) m/s = 22.22 m/s)
a = acceleration (constant deceleration of 3.24 m/s^2)
t = time
Rearranging the equation to solve for time (t):
t = (vf - vi) / a
Substituting the values into the equation:
t = (0 - 22.22) / (-3.24)
t = 6.85 seconds (approx.)
Therefore, it will take approximately 6.85 seconds for the car to come to a complete stop.
To find the distance (d) traveled before stopping, we can use another equation of motion:
d = vit + (1/2)at^2
Where:
d = distance
vi = initial velocity
t = time
a = acceleration
Substituting the values into the equation:
d = (22.22)(6.85) + (1/2)(-3.24)(6.85)^2
Simplifying the equation using the values:
d = 152.13 meters (approx.)
Therefore, the car will travel approximately 152.13 meters before coming to a complete stop.