The mass of a minibus with the driver is 1.50×10^3 kg.Assume that the passengers have an average mass of 50.0kg each.The driver is moving at a speed of 30.0m.s^-1 when he notices that the traffic lights ahead have turned to red.He applies a force of 9000N on the brake pedal.
a)how far must he have been from the traffic lights if he were able to stop in time?
b)how long will it take him to stop?
c)how will the stopping distance change if the minibus is carrying 10 passengers
a) a = F/m = 9000/1500
x = v^2/(2*a)
b) t = v/a
c) Add 500 to mass in part a & repeat
how long it will take him to stop
a) To find the distance the minibus must have been from the traffic lights, we can use the equation for stopping distance:
Stopping distance = (initial velocity^2) / (2 * acceleration)
The initial velocity is 30.0 m/s, and the acceleration can be calculated using Newton's second law:
Force = mass * acceleration
From this equation, we can solve for acceleration:
acceleration = Force / mass
The mass of the minibus is 1.50 × 10^3 kg. Plugging in the values, we have:
acceleration = 9000 N / 1500 kg = 6 m/s^2
Now we can calculate the stopping distance:
Stopping distance = (30.0 m/s)^2 / (2 * 6 m/s^2)
Stopping distance = 450 m
Therefore, the minibus must have been 450 meters from the traffic lights to stop in time.
b) To find the time it will take him to stop, we can use the equation:
Time = velocity / acceleration
Plugging in the values, we have:
Time = 30.0 m/s / 6 m/s^2
Time = 5 s
Therefore, it will take him 5 seconds to stop.
c) To find out how the stopping distance changes if the minibus is carrying 10 passengers, we need to recalculate the mass of the minibus. With the driver, the mass is 1.50 × 10^3 kg. Adding 10 passengers with an average mass of 50.0 kg each:
Mass of minibus with passengers = 1.50 × 10^3 kg + 10 passengers * 50.0 kg/passenger
Mass of minibus with passengers = 2000 kg
Now we need to calculate the new acceleration using the updated mass:
acceleration = Force / mass
acceleration = 9000 N / 2000 kg
acceleration = 4.5 m/s^2
Using the same equation as before, we can calculate the new stopping distance:
Stopping distance = (30.0 m/s)^2 / (2 * 4.5 m/s^2)
Stopping distance = 100 m
Therefore, if the minibus is carrying 10 passengers, the stopping distance will be 100 meters.
To solve these questions, we need to use the principles of Newton's laws of motion. Let's break down each question and explain the steps to find the answers.
a) How far must he have been from the traffic lights if he was able to stop in time?
To calculate the stopping distance, we need to consider the force (in Newtons) applied by the driver to the brake pedal. According to Newton's second law (F = ma), the force applied leads to an acceleration (a) experienced by the minibus.
First, let's calculate the total mass of the minibus and the passengers:
Mass of minibus = 1.50 × 10^3 kg
Number of passengers = 10
Average mass of each passenger = 50.0 kg
Total mass = Mass of minibus + (Number of passengers × Average mass of each passenger)
Total mass = 1.50 × 10^3 kg + (10 × 50.0 kg)
Now, with the total mass calculated, we can find the acceleration (a) using Newton's second law. Rearranging the formula, we get a = F / m.
Acceleration = Force applied / Total mass
Substituting the given values:
Acceleration = 9000 N / (1.50 × 10^3 kg + (10 × 50.0 kg))
Once we have the acceleration, we can use the formula of motion to find the stopping distance. The formula for distance is given by d = (v^2 - u^2) / (2a), where:
- d is the stopping distance
- v is the final velocity (0 m/s as the minibus needs to stop)
- u is the initial velocity (30.0 m/s)
- a is the acceleration calculated in the previous step
Substituting the given values and solving for d:
Stopping distance = (0^2 - 30.0^2) / (2 × Acceleration)
b) How long will it take him to stop?
To calculate the time it takes to stop, we'll use the formula of motion t = (v - u) / a, where:
- t is the time taken to stop
- v is the final velocity (0 m/s)
- u is the initial velocity (30.0 m/s)
- a is the acceleration calculated previously
Substituting the given values:
Time taken to stop = (0 - 30.0) / Acceleration
c) How will the stopping distance change if the minibus is carrying 10 passengers?
Since the stopping distance depends on the total mass of the minibus and its passengers, adding 10 passengers will increase the total mass. Consequently, the stopping distance will increase proportionally.
To calculate the new stopping distance, follow the same steps explained in (a) using the updated total mass of the minibus and passengers.