Shawn and his bike have a total mass of
58.5 kg. Shawn rides his bike 0.54 km in 17.2 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.
Use equations: KE=.5*m*v^2 and v=d/t
KE=.5*m*(d/t)
KE=.5*58.5*(540/(17.2*60))
KE=15.3 J
To calculate Shawn's kinetic energy, we need to use the formula:
K.E. = 1/2 * m * v^2
Where:
K.E. represents kinetic energy,
m represents mass, and
v represents velocity.
First, let's convert the distance Shawn rides his bike from kilometers (km) to meters (m) since the acceleration of gravity is given in meters per second (m/s). We know that 1 km = 1000 m, so:
0.54 km = 0.54 * 1000 m = 540 m
Next, let's convert the time from minutes (min) to seconds (s) since velocity is given in m/s. We know that 1 min = 60 s, so:
17.2 min = 17.2 * 60 s = 1032 s
Now, we can calculate the velocity by dividing the distance by the time:
v = distance / time = 540 m / 1032 s ≈ 0.52 m/s
Now, substitute the given values into the kinetic energy formula:
K.E. = 1/2 * m * v^2
Since Shawn and his bike have a total mass of 58.5 kg:
K.E. = 1/2 * 58.5 kg * (0.52 m/s)^2
Simplifying:
K.E. = 1/2 * 58.5 kg * 0.27 m^2/s^2
K.E. ≈ 7.5295 kg·m^2/s^2
One Joule (J) is equivalent to a kilogram-meter squared per second squared (kg·m^2/s^2). Therefore, the kinetic energy is approximately:
K.E. ≈ 7.5295 J
So Shawn's kinetic energy is approximately 7.5295 Joules (J).