Traveling at a speed of 16.1 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 0.720. What is the speed of the automobile after 1.30 s have elapsed? Ignore the effects of air resistance.
Vf=Vo+a*t where a= force/mass=mg*mu/mass=-.720*9.8 m/s^2
solve for vf, given t.
To find the speed of the automobile after 1.30 s have elapsed, we can use the equation for acceleration:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (v₀) = 16.1 m/s
Time (t) = 1.30 s
The final velocity is what we need to find.
First, we need to calculate the deceleration caused by friction using the equation:
frictional force = (coefficient of kinetic friction) × (normal force)
Using the equation for frictional force:
frictional force = mass × acceleration
Since only the weight of the car is acting as the normal force, we can rewrite the equation as:
frictional force = mass × gravitational acceleration
Then, using the equation for net force:
frictional force = mass × acceleration
The net force is given by:
net force = mass × acceleration
The net force is also equal to the frictional force, so we can write:
net force = frictional force
Now, we can calculate the acceleration:
acceleration = net force / mass
acceleration = (frictional force) / mass
From the equation of motion:
v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled. Assuming the distance traveled is negligible (since we are looking at the velocity after a short amount of time), we can simplify the equation to:
v = √(u² + 2as)
Rearranging the equation for acceleration:
a = (final velocity - initial velocity) / time
Squaring both sides of the equation and rearranging:
(final velocity - initial velocity) = 2a × time
Now we can substitute in the known values:
(0 - 16.1) m/s = 2 × acceleration × 1.30 s
Solving for acceleration:
acceleration = (0 - 16.1) / (2 × 1.30)
Finally, we can substitute the calculated acceleration back into the equation to find the final velocity:
final velocity = √(initial velocity² + 2 × acceleration × distance)
final velocity = √(16.1² + 2 × acceleration × 1.30)
final velocity = √(259.21 + 2 × (-6.19) × 1.30)
final velocity = √(259.21 - 16.06)
final velocity = √243.15
final velocity ≈ 15.61 m/s
Therefore, the speed of the automobile after 1.30 s have elapsed is approximately 15.61 m/s.
To find the speed of the automobile after 1.30 seconds have elapsed, we can use the equation of motion that relates initial velocity, time, acceleration, and final velocity.
The equation we can use is:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is 16.1 m/s and the final velocity (v) is what we are trying to find. Since the driver suddenly locks the wheels by slamming on the brakes, the acceleration (a) will be determined by the coefficient of kinetic friction between the tires and the road.
The formula to calculate acceleration is:
a = μ * g
Where:
a = acceleration
μ = coefficient of kinetic friction
g = acceleration due to gravity (approximately 9.8 m/s^2)
In this case, the coefficient of kinetic fiction (μ) is 0.720.
First, we calculate the acceleration:
a = 0.720 * 9.8
a ≈ 7.056 m/s^2
Now, we can substitute the values of initial velocity (u), acceleration (a), and time (t) into the equation:
v = u + at
v = 16.1 + (7.056 * 1.30)
v ≈ 25.45 m/s
Therefore, the speed of the automobile after 1.30 seconds have elapsed would be approximately 25.45 m/s.