a driver of a 1200-kg car notices that the car slows from 20 m/s to 15 m/s as it coasts a distance of 130 m along level ground. How large a force opposes the motion? Show the solution
Given:
m = 1200kg
u = 20m/s
v = 15m/s
s = 130m
Use:
v = u + at
s = ut + (at^2)/2
F = ma
Solve the velocity equation for time (t).
Substitute this into the displacement equation to solve for acceleration (a).
Multiply acceleration by mass (m) to give force (F).
To determine the force opposing the motion, we can use the equation:
Force = mass × acceleration
First, we need to find the acceleration of the car. We can use the equation:
acceleration = (final velocity - initial velocity) / time
Since we know the initial and final velocities, we need to find the time it takes for the car to slow down. We can use the equation:
distance = average velocity × time
In this case, the average velocity can be found by adding the initial and final velocities and dividing by 2:
average velocity = (initial velocity + final velocity) / 2
Given that the initial velocity (u) is 20 m/s, the final velocity (v) is 15 m/s, and the distance (s) is 130 m, we can find the average velocity and then calculate the time:
average velocity = (20 + 15) / 2 = 35 / 2 = 17.5 m/s
distance = average velocity × time
130 = 17.5 × time
Dividing both sides of the equation by 17.5, we find:
time = 130 / 17.5 ≈ 7.43 seconds
Now, we can calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (15 - 20) / 7.43
acceleration ≈ -0.67 m/s²
The negative sign indicates that the car is decelerating or slowing down.
Finally, we can calculate the force opposing the motion:
Force = mass × acceleration
Force = 1200 kg × -0.67 m/s²
Force ≈ -800 N
The force opposing the motion is approximately 800 N, and the negative sign indicates that it acts in the opposite direction of the car's motion.
To determine the force opposing the motion of the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Mass of the car, m = 1200 kg
Initial velocity, u = 20 m/s
Final velocity, v = 15 m/s
Distance covered, s = 130 m
We first need to calculate the acceleration of the car. The formula to calculate acceleration is:
acceleration (a) = (final velocity - initial velocity) / time
Since the car is coasting, there is no time provided. However, we can assume that the time taken is the same for both the initial and final velocities. Therefore, we can disregard time as it will cancel out in the calculations.
Now, let's calculate the acceleration:
acceleration (a) = (15 m/s - 20 m/s) / time
As we disregard time, we can simplify it to:
acceleration (a) = -5 m/s
The negative sign indicates that the car is decelerating.
Now, we can determine the force opposing the motion using the formula:
force (F) = mass (m) × acceleration (a)
Substituting the given values:
force (F) = 1200 kg × -5 m/s^2
Calculating:
force (F) = -6000 N
Therefore, the force opposing the motion of the car is 6000 Newtons in the opposite direction.