A cyclist was traveling at 5km/h when he observed a swarm of fierce bees behind him.He accelerates from 5Km/h to 42km/h within 15 seconds mass is 60kg and that of the bicycle 15 kg.calculate the 1.acceleration 2.acceleration mass 3.force required for the acceleration.
1. acceleration = change in speed / change in time
2. acceleration mass = rider mass + bicycle mass
3. force = mass * acceleration
... Newtons = kg * m/s^2
To calculate the requested values, we can use the formulas of acceleration, acceleration mass, and force.
1. Acceleration:
Acceleration is given by the formula:
acceleration = (final velocity - initial velocity) / time
Here, the initial velocity (u) is 5 km/h, the final velocity (v) is 42 km/h, and the time (t) is 15 seconds.
First, let's convert the velocities from km/h to m/s:
initial velocity = 5 km/h = 5 * (1000/3600) m/s = 1.39 m/s
final velocity = 42 km/h = 42 * (1000/3600) m/s = 11.67 m/s
Now, we can calculate the acceleration:
acceleration = (11.67 m/s - 1.39 m/s) / 15 s = 0.64 m/s^2
Therefore, the acceleration is 0.64 m/s^2.
2. Acceleration Mass:
Acceleration mass is the mass on which the force is acting to produce the acceleration. In this case, it is the total mass of the cyclist and the bicycle.
acceleration mass = mass of cyclist + mass of bicycle
acceleration mass = 60 kg + 15 kg = 75 kg
Therefore, the acceleration mass is 75 kg.
3. Force Required for Acceleration:
The force required to produce acceleration is given by Newton's second law of motion, which states that force (F) equals mass (m) times acceleration (a).
force = acceleration mass * acceleration
force = 75 kg * 0.64 m/s^2 = 48 N
Therefore, the force required for the acceleration is 48 N.
To calculate the required values, we can use the provided information. Let's break down each calculation step by step:
1. Acceleration:
Acceleration is the rate of change of velocity. We can use the formula:
Acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 5 km/h = 5,000 m / (60 * 60)s = 1.39 m/s
Final velocity (v) = 42 km/h = 42,000 m / (60 * 60)s = 11.67 m/s
Time (t) = 15 seconds
Using the formula:
Acceleration = (11.67 m/s - 1.39 m/s) / 15 s
Acceleration = 10.28 m/s / 15 s
Acceleration = 0.685 m/s²
Therefore, the acceleration of the cyclist is 0.685 m/s².
2. Acceleration Mass:
The acceleration mass can be calculated using the formula:
Acceleration Mass = (bike mass + rider mass)
Given:
Bike mass = 15 kg
Rider mass = 60 kg
Using the formula:
Acceleration Mass = 15 kg + 60 kg
Acceleration Mass = 75 kg
Therefore, the acceleration mass (mass of the cyclist and bike) is 75 kg.
3. Force Required for Acceleration:
To calculate the force required for acceleration, we use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Given:
Acceleration (a) = 0.685 m/s²
Mass (m) = 75 kg
Using the formula:
Force = 75 kg * 0.685 m/s²
Force = 51.375 N
Therefore, the force required for acceleration is 51.375 Newtons.