A 600kg car is moving on a level road at 30m/s.how large is a retarding force is required to stop it in a distance of 70m
To calculate the retarding force required to stop the car, we can use the equation:
Force = mass × acceleration
First, let's calculate the acceleration of the car using the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (which is 0 m/s since the car needs to stop)
u = initial velocity (30 m/s)
s = distance (70 m)
Rearranging the equation, we have:
0 = (30)^2 + 2 × a × 70
900 = 140a
a = 900/140 ≈ 6.43 m/s^2
Now that we have the acceleration, we can calculate the retarding force using the formula:
Force = mass × acceleration
Force = 600 kg × 6.43 m/s^2
Force ≈ 3860 N
Therefore, a retarding force of approximately 3860 Newtons is required to stop the 600 kg car in a distance of 70 meters.
To find the retarding force required to stop the car, we can use the concept of force and the equations of motion.
The equation that relates force, mass, and acceleration is:
Force = mass × acceleration
In this case, the acceleration of the car when it is being stopped is negative because it is opposing the motion of the car. So, we can rewrite the equation as:
Force = mass × (-acceleration)
To find the acceleration, we can use the second equation of motion, which relates distance, initial velocity, final velocity, and acceleration:
final velocity^2 = initial velocity^2 + 2 × acceleration × distance
Here, the final velocity is zero since we want to stop the car, the initial velocity is 30 m/s, and the distance is 70 m. We rearrange the equation to solve for acceleration:
acceleration = (final velocity^2 - initial velocity^2) / (2 × distance)
Substituting the given values:
acceleration = (0^2 - 30^2) / (2 × 70)
acceleration = (-900) / 140
acceleration = -6.43 m/s^2
Now, substituting this value of acceleration and the mass (600 kg) into the force equation, we can find the retarding force:
Force = mass × acceleration
Force = 600 kg × (-6.43 m/s^2)
Force = -3,858 N (rounded to the nearest whole number)
Therefore, a retarding force of approximately 3,858 Newtons is required to stop the car in a distance of 70 meters.
speed:
v = 30 + a t
what is a when v = 0
-30 = a t
a = -30/t
distance:
70 = 30 t + (1/2) a t^2
70 = 30 t -(15/t) t^2
70 = 15 t
t = 14/3 seconds to stop
a = -30/t = -90/14 m/s^2 = -45/7
then F = m a
F = -600 (45/7) Newtons
There is a quicker way:
vf^2=vi^2+2ad but a= forcefriction/mass
0=30^2+2*force/mass * 70
solve for force.