The mass of a minibus with the driver is 1500kg. Assume that the passengers have an average mass of 50 kg each .The minibus is moving at a speed of 30 m/s when he notices that the traffic lights ahead have turned red. He replied a force of 900N on the brake pedal.
1. Calculate the deceleration if the taxis empty, that is, there were no passengers .
2. How long will it take him to stop ?
3. How will the stopping distance change if the minibus is carrying 10 passengers?
1. Well, if the minibus is empty and the driver applies a force of 900N on the brake pedal, the deceleration can be calculated using Newton's second law, which states that force equals mass multiplied by acceleration. Since the mass of the minibus is 1500kg, and there are no passengers, the total mass is still 1500kg. Therefore, the deceleration is given by the formula: acceleration = force / mass = 900N / 1500kg = 0.6 m/s².
2. To calculate the time it takes for the minibus to stop, we can use the equation of motion: final velocity = initial velocity + (acceleration * time). Since the minibus is coming to a stop, the final velocity is 0 m/s. The initial velocity is 30 m/s, and the acceleration is 0.6 m/s². Plugging these values into the equation, we get 0 = 30 + (0.6 * time). Solving for time, we find that it will take approximately 50 seconds for the minibus to stop.
3. Now, let's consider the minibus carrying 10 passengers, each with an average mass of 50 kg. The total mass of the minibus and passengers would be: 1500kg + (10 passengers * 50kg/passenger) = 2000kg. Using the same formula as before, force equals mass multiplied by acceleration. With a force of 900N and a mass of 2000kg, the deceleration would now be: acceleration = force / mass = 900N / 2000kg = 0.45 m/s². So, with more weight on board, the deceleration would decrease.
Regarding the stopping distance, it would mainly depend on the deceleration and the initial speed of the minibus. However, since the deceleration has decreased with the additional weight, it would take the minibus a longer distance to stop. In other words, the stopping distance would increase compared to when the minibus was empty. This is assuming the braking force and other factors remain constant.
1. To calculate the deceleration, we can 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 (F = ma).
Since the minibus is empty and there are no passengers, the total mass of the minibus is 1500 kg (including the driver).
Given that the force applied on the brake pedal is 900 N, we can rearrange the equation to find the deceleration (a):
a = F/m
a = 900 N / 1500 kg
a = 0.6 m/s²
So, the deceleration when the minibus is empty is 0.6 m/s².
2. To calculate the time it takes for the minibus to stop, we can use one of the kinematic equations of motion:
v = u + at
where:
- v is the final velocity (0 m/s in this case, since the minibus stops)
- u is the initial velocity (30 m/s)
- a is the acceleration (0.6 m/s²)
- t is the time we want to find
Rearranging the equation, we get:
t = (v - u) / a
t = (0 - 30) / -0.6
t = 50 seconds
So, it will take the minibus 50 seconds to stop.
3. To calculate how the stopping distance changes when the minibus carries 10 passengers, we need to consider the additional mass of the passengers.
Each passenger has an average mass of 50 kg, so 10 passengers have a combined mass of 10 * 50 kg = 500 kg.
The total mass of the minibus with the 10 passengers is now 1500 kg (mass of the minibus and the driver) + 500 kg (mass of the passengers) = 2000 kg.
Using the same deceleration calculated in question 1 (0.6 m/s²), we can use the following equation to find the stopping distance (d):
d = (v² - u²) / (2a)
where:
- v is the final velocity (0 m/s)
- u is the initial velocity (30 m/s)
- a is the deceleration (0.6 m/s²)
Plugging in the values, we get:
d = (0² - 30²) / (2 * -0.6)
d = -900 / -1.2
d = 750 meters
So, the stopping distance will be 750 meters when the minibus is carrying 10 passengers.
To calculate the deceleration of the minibus, we need to use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
1. To calculate the deceleration with no passengers, we can assume that the force applied by the driver on the brake pedal is equal to the force of friction between the tires and the road. So, we can use the equation F = ma to solve for acceleration (a).
Given:
Mass of minibus (m) = 1500 kg
Force applied (F) = 900 N
Rearranging the equation, we have:
a = F/m
a = 900 N / 1500 kg
a = 0.6 m/s^2
Therefore, the deceleration of the minibus when it's empty is 0.6 m/s^2.
2. To calculate the time it will take for the minibus to stop, we can use the equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (30 m/s), a is the deceleration, and t is the time.
Rearranging the equation, we have:
t = (v - u) / a
t = (0 m/s - 30 m/s) / (-0.6 m/s^2)
t = 50 s
Therefore, it will take 50 seconds for the minibus to stop.
3. To find out how the stopping distance changes when the minibus is carrying 10 passengers, we need to consider the impact of the additional mass on the deceleration.
First, we calculate the total mass of the minibus and passengers:
Mass of minibus without passengers = 1500 kg
Mass of each passenger = 50 kg
Number of passengers = 10
Total mass = Mass of minibus + (Mass of each passenger * Number of passengers)
= 1500 kg + (50 kg * 10)
= 2000 kg
Now, we need to find the new deceleration using the same formula as before, F = ma, but with the updated total mass.
Force applied (F) remains the same: 900 N.
Total mass (m) = 2000 kg
Deceleration (a) = F / m
= 900 N / 2000 kg
= 0.45 m/s^2
So, when the minibus is carrying 10 passengers, the deceleration is 0.45 m/s^2.
The stopping distance is determined by the deceleration and the initial velocity.
We know that the deceleration (a) is 0.45 m/s^2, and the initial velocity (u) is 30 m/s. Using the formula, v^2 = u^2 + 2as, we can solve for s, the stopping distance. Rearranging the formula, we have:
s = (v^2 - u^2) / (2a)
s = (0 - 30^2) / (2 * 0.45)
s = -900 / 0.9
s = -1000 m
The negative sign indicates that the stopping distance is in the opposite direction of the motion. Therefore, the stopping distance is 1000 meters when the minibus is carrying 10 passengers.