The car traveling at 50.0 m/s in a circular path with a radius of 400 m has a centripetal acceleration of 6.25 m/s², an angular speed of 0.125 rad/s, and a tangential acceleration of 4.0 m/s².
When a car is traveling in a circular path, it experiences centripetal acceleration that keeps it moving along the curve. To find the magnitude of this acceleration for a car with a radius of curvature of 400 m and a speed of 50.0 m/s, we use the formula:
ac = v2 / r
Substituting the given values:
ac = (50.0 m/s)2 / 400 m = 6.25 m/s2
Angular Speed
Angular speed (ω) can be calculated using:
ω = v / r
For a speed of 50.0 m/s and radius 400 m:
ω = 50.0 m/s / 400 m = 0.125 rad/s
Tangential Acceleration
The tangential acceleration (at) is the rate of change of the velocity with respect to time. Using the given uniform acceleration:
at = Δv / Δt
From 40.0 m/s to 60.0 m/s in 5.00 s:
at = (60.0 m/s – 40.0 m/s) / 5.00 s = 4.0 m/s2
The centripetal and tangential accelerations are components of the total acceleration experienced by an object in circular motion. Together, they can be used to calculate the total acceleration of an object moving along a curved path.