Traveling at a speed of 14.3 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the road is 0.730. What is the speed of the automobile after 1.15 s have elapsed? Ignore the effects of air resistance.
To find the speed of the automobile after 1.15 s have elapsed, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is given as 14.3 m/s, and we need to find the final velocity (v) after 1.15 s.
To find the acceleration (a), we can use the formula:
a = μ * g
Where:
a = acceleration
μ = coefficient of kinetic friction
g = acceleration due to gravity (approximately 9.8 m/s²)
In this case, the coefficient of kinetic friction (μ) is given as 0.730.
So, plugging in the values:
a = 0.730 * 9.8
a = 7.154 m/s² (approx)
Now we can substitute the values into the equation of motion:
v = 14.3 + (7.154 * 1.15)
v = 14.3 + 8.2271
v = 22.5271 m/s (approx)
Therefore, the speed of the automobile after 1.15 s have elapsed is approximately 22.53 m/s.
To find the speed of the automobile after 1.15 s have elapsed, we need to use the laws of motion and apply the concept of kinetic friction.
First, let's identify the given information:
- Initial speed (v0) = 14.3 m/s
- Time (t) = 1.15 s
- Coefficient of kinetic friction (μ) = 0.730
We can use the following equation of motion to calculate the final speed (v) when the wheels lock:
v = v0 - μ * g * t
Where:
- v is the final speed
- v0 is the initial speed
- μ is the coefficient of kinetic friction
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time elapsed
Now let's substitute the given values into the equation:
v = 14.3 m/s - (0.730 * 9.8 m/s^2 * 1.15 s)
Calculate the expression within the parentheses:
v = 14.3 m/s - (8.116 m/s^2 * 1.15 s)
v = 14.3 m/s - 9.3434 m/s
v = 4.9566 m/s
Therefore, the speed of the automobile after 1.15 s have elapsed is approximately 4.96 m/s (rounded to two decimal places).