A car of mass 1200 kg is brought to rest from a speed of 20 ms^-1 by a constant braking force 3000 N. calculate the retardation and the time the car takes to come to rest. (Force F=3000N, since force applied is to bring the car to rest).
a = f / m = 3000 N / 1200 kg = 2.5 m/s^2
t = v / a = 20 m/s / 2.5 m/s^2 = 8 s
To find the retardation and the time it takes for the car to come to rest, we will apply Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma).
First, we need to find the retardation (acceleration). We know the force applied (F) is 3000 N, and the mass (m) is 1200 kg. Rearranging the equation, we have:
a = F / m
a = 3000 N / 1200 kg
a ≈ 2.5 m/s²
The retardation of the car is approximately 2.5 m/s².
Now, we can calculate the time it takes for the car to come to rest using the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s since the car comes to rest)
u = initial velocity (20 m/s)
a = retardation (-2.5 m/s²)
Rearranging the equation, we have:
t = (v - u) / a
t = (0 - 20 m/s) / (-2.5 m/s²)
t = 8 seconds
Therefore, the car takes approximately 8 seconds to come to rest.
To solve this problem, we'll 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.
Step 1: Calculate the acceleration (retardation):
We know that the force (F) acting on the car is equal to the mass (m) of the car multiplied by its acceleration (a):
F = m * a
Rearranging the equation, we have:
a = F / m
Here, F = 3000 N and m = 1200 kg.
Substituting these values into the equation, we get:
a = 3000 N / 1200 kg
a = 2.5 m/s²
Therefore, the retardation of the car is 2.5 m/s².
Step 2: Calculate the time taken to come to rest:
We can use the formula of motion:
v² = u² + 2a s
where:
v = final velocity (0 m/s since the car comes to rest)
u = initial velocity (20 m/s)
a = acceleration/retardation (-2.5 m/s², negative because the car is slowing down)
s = distance covered (unknown)
Rearranging the equation, we get:
0² = 20² + 2(-2.5) s
0 = 400 - 5s
5s = 400
s = 400 / 5
s = 80 meters
Now, we can use the formula of motion:
v = u + at
where:
v = final velocity (0 m/s)
u = initial velocity (20 m/s)
a = acceleration/retardation (-2.5 m/s²)
t = time taken (unknown)
Rearranging the equation, we have:
0 = 20 + (-2.5) t
-2.5t = -20
t = -20 / -2.5
t = 8 seconds
Therefore, the car takes 8 seconds to come to rest.
To summarize:
The retardation of the car is 2.5 m/s², and it takes 8 seconds to come to rest.