A 600 kg car is moving on a level road at 30 m/s. How large of a braking force is needed to stop it in a distance of 75m?
V^2 = Vo^2 + 2a*d
V = 0
Vo = 30 m/s.
d = 75 m.
Solve for a.(It should be negative).
F = m*a. The force will be negative,
because it acts against the motion.
To calculate the braking force needed to stop the car, we can use the equation for acceleration:
\(a = \frac{{V_f^2 - V_i^2}}{{2d}}\)
Where:
- \(a\) is the acceleration
- \(V_f\) is the final velocity (0 m/s, since the car needs to stop)
- \(V_i\) is the initial velocity (30 m/s)
- \(d\) is the distance (75 m)
First, let's calculate the acceleration:
\(a = \frac{{0^2 - 30^2}}{{2 \times 75}}\)
Simplifying the equation:
\(a = \frac{{-900}}{{150}}\)
\(a = -6 \, \text{m/s}^2\)
The negative sign indicates deceleration.
To calculate the braking force, we can use Newton's second law:
\(F = m \times a\)
Where:
- \(F\) is the force
- \(m\) is the mass (600 kg)
- \(a\) is the acceleration (-6 m/s^2)
Plugging in the values:
\(F = 600 \times -6\)
\(F = -3600 \, \text{N}\)
The negative sign indicates that the force is in the opposite direction of motion, which is the braking force needed to stop the car. Therefore, a braking force of 3600 N is needed to stop the car in a distance of 75 m.
To calculate the braking force needed to stop the car, we need to use the equation:
Force = (mass × acceleration)
First, let's find the acceleration by using the following equation of motion:
(vf^2) = (vi^2) + 2as
Where:
vf = final velocity (which is 0 when the car stops)
vi = initial velocity (given as 30 m/s)
a = acceleration (unknown)
s = distance (given as 75m)
Rearranging the equation, we get:
a = (vf^2 - vi^2) / (2s)
Since the final velocity (vf) is 0 m/s, the equation becomes:
a = (- vi^2) / (2s)
Now, let's plug in the values:
a = (-30^2) / (2 × 75)
Calculate the value:
a = (-900) / 150
a = -6 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the car's motion. In this case, it represents deceleration since the car is slowing down.
Now, we can plug the mass (m) and acceleration (a) into the force equation:
Force = mass × acceleration
= 600 kg × (-6 m/s^2)
Calculate the value:
Force = -3600 N
The negative sign indicates that the force is in the opposite direction to the car's motion, which makes sense since it is a braking force that opposes the car's velocity. Therefore, a braking force of 3600 Newtons is needed to stop the car in a distance of 75 meters.