Shawn and his bike have a total mass of
57.1 kg. Shawn rides his bike 1.3 km in 14 min
at a constant velocity.
The acceleration of gravity is 9.8 m/s
2
.
What is Shawn’s kinetic energy?
g is not required if the bike is on a horizontal road.
velocity = 1.3*10^3 m / (14 min * 60 s/min)
= (65/42) m/s
Kinetic energy
= (1/2)mv^2
= (1/2)(57.1)(65/42)^2 J
To find Shawn's kinetic energy, we need to calculate his velocity first. Given that he rides his bike at a constant velocity and covers a distance of 1.3 km in 14 minutes, we can convert the distance and time to SI units.
1. Convert 1.3 km to meters:
1.3 km * 1000 m/km = 1300 m
2. Convert 14 minutes to seconds:
14 min * 60 s/min = 840 s
Now we have the distance, time, and acceleration (gravity). We can calculate Shawn's velocity using the equation:
Velocity = Distance / Time
Velocity = 1300 m / 840 s
Velocity ≈ 1.55 m/s
Next, we can calculate Shawn's kinetic energy using the equation:
Kinetic energy = (1/2) * mass * velocity^2
Since the total mass of Shawn and his bike is given as 57.1 kg, we can substitute the values into the equation:
Kinetic energy = (1/2) * 57.1 kg * (1.55 m/s)^2
Calculating this expression, we get:
Kinetic energy ≈ 56.6 J
Therefore, Shawn's kinetic energy is approximately 56.6 Joules.
To find Shawn's kinetic energy, we need to use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given information:
- Mass (m) = 57.1 kg
- Distance traveled (d) = 1.3 km
- Time (t) = 14 min
- Acceleration due to gravity (g) = 9.8 m/s^2
First, let's convert the distance from kilometers to meters:
1 kilometer = 1000 meters
So, the distance traveled (d) = 1.3 km * 1000 = 1300 meters.
Next, we need to convert time from minutes to seconds, since the units for acceleration (m/s^2) are in the SI system:
1 minute = 60 seconds
So, the time (t) = 14 min * 60 = 840 seconds.
To calculate the velocity, we'll use the formula:
Velocity (v) = distance / time
v = 1300 meters / 840 seconds = 1.547 m/s
Now, we can plug the values into the kinetic energy formula:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 57.1 kg * (1.547 m/s)^2
To calculate, we need to first square the velocity and then multiply it by the mass:
Kinetic Energy = (1/2) * 57.1 kg * 2.391 m^2/s^2
Next, we multiply the mass by the squared velocity:
Kinetic Energy = 68.658 kg * m^2/s^2
Finally, we can simplify the unit of measurement:
Kinetic Energy = 68.658 Joules (J)
According to the given information and calculations, Shawn's kinetic energy is approximately 68.658 Joules.