An automobile of mass 2000 kg moving at 30 m/s suddenly stopped with a constant braking
force of 10000 N. How far does the car travel before stopping?
F = M*a.
a = F/M = -10,000/2000 = -5m/s^2.
V^2 = Vo^2 + 2a*d.
0 = 30^2 - 10d.
d = ?.
To find the distance the car travels before stopping, we can use the equations of motion. Here's a step-by-step solution:
Step 1: Find the acceleration of the car.
We can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). Rearranging the equation, we have:
acceleration (a) = force (F) / mass (m)
Given:
Force (F) = 10000 N
Mass (m) = 2000 kg
Substituting the given values into the equation:
acceleration (a) = 10000 N / 2000 kg
acceleration (a) = 5 m/s^2
Step 2: Find the time taken to stop.
Using the equation of motion: v = u + at, where:
v = final velocity (0 m/s, as the car stops)
u = initial velocity (30 m/s)
a = acceleration (5 m/s^2)
t = time taken
Rearranging the equation to solve for time (t):
t = (v - u) / a
Substituting the values:
t = (0 - 30) / 5
t = -30 / 5
t = -6 seconds
Since time cannot be negative, we take the absolute value:
t = 6 seconds
Step 3: Find the distance traveled.
Using the equation of motion: s = ut + 0.5at^2, where:
s = distance traveled
u = initial velocity (30 m/s)
a = acceleration (5 m/s^2)
t = time taken (6 seconds)
Substituting the values:
s = (30 * 6) + (0.5 * 5 * 6^2)
s = 180 + (0.5 * 5 * 6^2)
s = 180 + (0.5 * 5 * 36)
s = 180 + (0.5 * 180)
s = 180 + 90
s = 270 meters
Therefore, the car travels a distance of 270 meters before stopping.
To find the distance the car travels before stopping, we can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, since the car stops)
u = initial velocity (30 m/s)
a = acceleration (caused by braking force)
s = distance traveled
First, let's calculate the acceleration:
F = ma
where:
F = braking force (10000 N)
m = mass of the car (2000 kg)
a = acceleration
So, rearranging the formula, we have:
a = F / m
Substituting the given values, we get:
a = 10000 N / 2000 kg
a = 5 m/s^2
Now, we can use the equation of motion to find the distance traveled:
0^2 = (30 m/s)^2 + 2 * 5 m/s^2 * s
Simplifying the equation:
900 = 600 + 10s
Rearranging to solve for s:
10s = 900 - 600
10s = 300
Dividing both sides by 10:
s = 300 / 10
s = 30 meters
Therefore, the car travels a distance of 30 meters before stopping.