Shawn and his bike have a total mass of
40.6 kg. Shawn rides his bike 1.9 km in
10.9 min at a constant velocity.
The acceleration of gravity is 9.8 m/s
2
.
What is Shawn’s kinetic energy?
Answer in units of J.
KE=1/2 m v^2=1/2 * 40.6 * (1900/(60*10.9))^2=171 joules check that
To calculate Shawn's kinetic energy, we first need to find his velocity. We can use the equation:
Velocity = Distance / Time
Given that Shawn rides his bike 1.9 km in 10.9 min, we need to convert these values to meters and seconds respectively:
Distance = 1.9 km = 1.9 * 1000 m = 1900 m
Time = 10.9 min = 10.9 * 60 s = 654 s
Now, we can calculate the velocity:
Velocity = 1900 m / 654 s
After performing the division, we get:
Velocity ≈ 2.906 m/s
Next, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * Mass * Velocity^2
Given that the mass of Shawn and his bike is 40.6 kg, and the velocity we just calculated is 2.906 m/s, we can substitute these values into the formula:
Kinetic Energy = (1/2) * 40.6 kg * (2.906 m/s)^2
Simplifying the right side of the equation:
Kinetic Energy ≈ 0.5 * 40.6 kg * 8.422 m^2/s^2
Lastly, we can perform the multiplication:
Kinetic Energy ≈ 169.273 J
Therefore, Shawn's kinetic energy is approximately 169.273 J.
To find Shawn's kinetic energy, we need to use the formula for kinetic energy:
Kinetic energy (KE) = (1/2) * mass * velocity^2
First, let's convert the given velocity from km/min to m/s:
1.9 km = 1.9 * 1000 m = 1900 m
10.9 min = 10.9 * 60 s = 654 s
Velocity = distance / time
Velocity = 1900 m / 654 s = 2.907 m/s
Now, we can substitute the values into the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
KE = (1/2) * 40.6 kg * (2.907 m/s)^2
KE = (1/2) * 40.6 kg * 8.431 m^2/s^2
Now, let's calculate the value:
KE = 0.5 * 40.6 kg * 8.431 m^2/s^2
KE = 171.2113 kg * m^2/s^2
Finally, let's express the answer in units of Joules (J):
1 J = 1 kg * m^2/s^2
Therefore, Shawn's kinetic energy is approximately 171.2113 J.