A 2000 kg car is slowed down uniformly from 18.0 m/s to 5.00 m/s in 4.20 s. (a) What average total force acted on the car during that time? (b) How far did the car travel during that time?
a) Oh, the poor car had to experience some slow-down action! To find the average total force, we can use Newton's second law, which states that force equals mass times acceleration. The acceleration can be calculated by taking the change in velocity and dividing it by the time it took, so we have:
acceleration = (final velocity - initial velocity) / time
acceleration = (5.00 m/s - 18.0 m/s) / 4.20 s
Now, the average total force can be found by multiplying the mass of the car with the acceleration:
average total force = mass * acceleration
average total force = 2000 kg * [(5.00 m/s - 18.0 m/s) / 4.20 s]
b) To find the distance traveled by the car, we can use the equation:
distance = (initial velocity + final velocity) / 2 * time
Therefore, the distance traveled by the car is:
distance = [(18.0 m/s + 5.00 m/s) / 2] * 4.20 s
Now, let me calculate these values for you!
To solve this problem, we can use the equations of motion. Let's start with part (a) and find the average total force that acted on the car during that time.
Step 1: Find the acceleration of the car using the equation:
acceleration (a) = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 18.0 m/s
Final velocity (v) = 5.00 m/s
Time (t) = 4.20 s
Substituting these values into the equation, we get:
a = (5.00 - 18.0) / 4.20
Step 2: Calculate the acceleration.
a = -12.0 / 4.20
Step 3: Determine the average force acting on the car using Newton's second law:
Force (F) = mass (m) × acceleration (a)
Given:
Mass (m) = 2000 kg
Substituting the values into the equation, we have:
F = 2000 × (-12.0 / 4.20)
Step 4: Calculate the average force.
F = -5730 N
Therefore, the average total force that acted on the car during that time is -5730 N.
Moving on to part (b), let's find the distance the car traveled during that time.
Step 1: Use the equation of motion:
distance (s) = initial velocity (u) × time (t) + 0.5 × acceleration (a) × time (t)^2
Given:
Initial velocity (u) = 18.0 m/s
Time (t) = 4.20 s
Acceleration (a) = -12.0 m/s^2
Substituting these values into the equation, we get:
s = 18.0 × 4.20 + 0.5 × (-12.0) × (4.20)^2
Step 2: Calculate the distance.
s = 75.6 - 101.64
s = -26.04 m
Therefore, the car traveled a distance of -26.04 m. The negative sign indicates that the car traveled in the opposite direction of the initial velocity.
To find the answers to these questions, we need to use the equations of motion and Newton's second law of motion. Let's break down the problem step by step:
Part (a): What average total force acted on the car during that time?
According to Newton's second law of motion, the force acting on an object can be calculated using the formula:
Force = Mass x Acceleration
In this case, the acceleration is given by the change in velocity divided by the time:
Acceleration = (Final velocity - Initial velocity) / Time
First, let's calculate the acceleration:
Acceleration = (5.00 m/s - 18.0 m/s) / 4.20 s
Acceleration = -12.00 m/s / 4.20 s
Acceleration = -2.86 m/s²
Since the car is being slowed down, the acceleration is negative.
Next, we can calculate the average total force using the formula:
Force = Mass x Acceleration
Force = 2000 kg x -2.86 m/s²
Force = -5720 N
Therefore, the average total force acting on the car during that time is -5720 N (N denotes Newton, the unit of force).
Part (b): How far did the car travel during that time?
To find the distance traveled by the car, we can use one of the equations of motion, namely:
Distance = Initial velocity x Time + (1/2) x Acceleration x Time²
In this case, the initial velocity is 18.0 m/s, the time is 4.20 s, and the acceleration is -2.86 m/s² (as calculated before).
Plugging these values into the equation:
Distance = 18.0 m/s x 4.20 s + (1/2) x -2.86 m/s² x (4.20 s)²
Distance = 75.6 m + (-27.23424 m)
Distance = 48.36576 m
Therefore, the car traveled approximately 48.37 meters during that time.
To summarize:
(a) The average total force acting on the car during that time is -5720 N (backward).
(b) The car traveled approximately 48.37 meters during that time.
v=v₀-at
a= (v₀-v)/t
(a)
F=ma
(b)
s= v₀t-at²/2