The Mass Of A Minibus with The Driver is 1500 kg.the Driver Is Moving At A Speed Of 30 m.s When He Notices That The traffic light Ahead Have turned To red.he Applies A Force Of 9000N on the brake pedal.

A)calculate his deceleration if the taxi is empty
B)how far must he be from the traffic lights if he were to stop in time?
C)how will the stopping distance change if the minibus is carrying 10 passengers if their average mass is 50kg each
D)How Long Will It Take Him To Stop

A) To calculate the deceleration, we can use Newton's second law of motion: F = ma, where F is the force, m is the mass, and a is the acceleration.

Given:
Mass of the minibus (m) = 1500 kg
Force applied (F) = 9000 N

Using the formula:
a = F / m
= 9000 N / 1500 kg
= 6 m/s^2

Therefore, the deceleration when the minibus is empty is 6 m/s^2.

B) To calculate the stopping distance, we can use the equation: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the stopping distance.

Given:
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -6 m/s^2 (negative sign as it is deceleration)

Using the formula:
v^2 = u^2 + 2as
0^2 = 30^2 + 2(-6)s
0 = 900 - 12s
12s = 900
s = 900 / 12

Therefore, the minibus must be 75 meters away from the traffic lights to stop in time.

C) When the minibus is carrying 10 passengers, we need to take into account their additional mass.

Average mass per passenger (m_p) = 50 kg
Number of passengers (n) = 10

Total additional mass (m_add) = m_p * n
= 50 kg * 10
= 500 kg

Total mass of minibus with passengers (m_total) = 1500 kg + 500 kg
= 2000 kg

The stopping distance is dependent on the mass, so with the additional passengers, the stopping distance will increase.

D) To calculate the time taken to stop, we can use the equation: t = (v - u) / a, where t is the time, v is the final velocity, u is the initial velocity, and a is the acceleration.

Given:
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -6 m/s^2

Using the formula:
t = (v - u) / a
t = (0 - 30) / (-6)
t = 30 / 6

Therefore, it will take him 5 seconds to stop completely.

A) To calculate the driver's deceleration when the minibus is empty, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). In this scenario, the force applied by the driver is 9000 N, and the mass of the minibus is 1500 kg. Rearranging the formula, we get acceleration (a) = F/m = 9000 N / 1500 kg = 6 m/s². Therefore, the deceleration of the minibus when empty is 6 m/s².

B) To find out how far the driver must be from the traffic lights in order to stop in time, we need to calculate the stopping distance. The stopping distance can be calculated using the formula: stopping distance = (initial velocity² - final velocity²) / (2 * acceleration). In this case, the initial velocity is 30 m/s (since the driver is moving at this speed) and the final velocity is 0 m/s (since the minibus needs to come to a complete stop). The acceleration was previously calculated as 6 m/s². Plugging in these values, the stopping distance = (30² - 0²) / (2 * 6) = 225 meters. Therefore, the driver must be at least 225 meters away from the traffic lights to stop in time.

C) If the minibus is now carrying 10 passengers, we need to account for their mass in the calculation. Each passenger has an average mass of 50 kg, so a total of 10 passengers would add an additional mass of 10 × 50 kg = 500 kg to the minibus. Adding this to the initial mass of the minibus (1500 kg), the new total mass would be 1500 kg + 500 kg = 2000 kg. Therefore, the stopping distance would change because the mass of the minibus has increased, affecting its deceleration. To calculate the new stopping distance, you would need to use similar calculations as in part B (using the new mass value) to find the total stopping distance for the minibus with passengers.

D) To calculate the time it will take for the minibus to stop, we can use the formula: time = (final velocity - initial velocity) / acceleration. In this case, the initial velocity is 30 m/s and the final velocity is 0 m/s (since the minibus needs to stop completely). The acceleration was previously calculated as 6 m/s². Plugging in these values, the time = (0 - 30) / (6) = -5 seconds. However, this negative sign indicates that the minibus would take 5 seconds to decelerate to a stop, assuming a constant deceleration. It is important to note that a negative sign is used to indicate deceleration in this case.

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