Traveling at a speed of 16.3 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 0.620. What is the speed of the automobile after 1.60 s have elapsed? Ignore the effects of air resistance.
Deceleration rate
a = (friction force)/mass
= M g 0.62/M = 0.62 g = 6.08 m/s^2
After t = 1.60 s,
V = Vo - a*t = 16.3 - 6.08*1.60
= 6.57 m/s
To find the speed of the automobile after 1.60 s have elapsed, we can use the equations of motion.
The first step is to calculate the deceleration of the automobile due to the frictional force. The force of kinetic friction can be calculated using the equation:
frictional force = coefficient of kinetic friction * normal force
Since the normal force is equal to the weight of the car (mg), we can substitute it into the equation:
frictional force = coefficient of kinetic friction * weight of car
Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
net force = mass * acceleration
In this case, the net force is the frictional force, and the acceleration is the deceleration of the car.
Therefore, we can write:
frictional force = mass * deceleration
Now, we can relate the deceleration to the change in velocity over time using the equation:
change in velocity = acceleration * time
Since we know the initial velocity of the car, we can calculate the final velocity using the equation:
final velocity = initial velocity + change in velocity
Applying these steps to the given problem:
1. Calculate the frictional force:
frictional force = coefficient of kinetic friction * weight of car
2. Calculate the deceleration of the automobile:
frictional force = mass * deceleration
3. Use the equation of motion to find the change in velocity:
change in velocity = acceleration * time
4. Calculate the final velocity:
final velocity = initial velocity + change in velocity
By following these steps and plugging in the given values, we can determine the speed of the automobile after 1.60 s have elapsed.