Velocities and Propagation of Errors
- a) Average velocity = (minimum velocity + maximum velocity) / 2
Minimum displacement = (13.3 – 0.4) m
= 12.9 m
Maximum time taken = 15.1 s
Minimum velocity = 12.9 m / 15.1 s
= 0.8543 m/s
Maximum displacement = (13.3 + 0.4) m
= 13.7 m.
Minimum time taken = (14.9 – 0.2) s
= 14.7 s
Maximum velocity = 13.7m / 14.7 s
Average velocity = (0.8543 + 0.9320)/2 m/s
= 0.89315 m/s
- b) Average velocity is the displacement over time, while the instantaneous velocity of an object is its velocity at a particular time. Average velocity of an object can equal its instantaneous velocity at any time if the object is traveling at a constant velocity. This can happen also at halfway of the objects trip whose acceleration is constant.
- c) Since constant acceleration is given by the equation:
Constant acceleration = ∆v / ∆t
The change in velocity is given by:
∆v = ∆t * const. acc.
Instantaneous velocity vi = initial velocity, Vo + ∆v
- a) The object might be moving at a constant positive acceleration, away from the origin.
- b) The object might be moving at a constant deceleration toward the origin.
- a ) Total displacement = 8.4 km +2.0 km
= 10.4 km.
- b) Time interval = time taken driving + time taken walking
Time taken driving = distance travelled / speed = 8.4 / 70 h
= 0.12 h.
Time taken walking = 30 /60 h = 0.5 h
Total time = (0.12+ 0.5) h
= 0.62 h
- c) Average velocity = the velocity while driving + walking velocity
Velocity while driving = 70 km/h
Velocity of walking = 2 km / 0.5 h
= 4 km/h
Average velocity = (70 + 4) / 2 km/h
= 74 / 2 km/h
= 37 km/h
Graphically, this is the average of the two velocities and yields 37 km/h.
- D) Average speed = total distance travelled / total time taken
Total distance = (8.4 + 2.0 + 2.0) = 12.4 km
Total time taken = (0.12 +0.50 +0.45) h = 1.07 h
Average speed = 12.4 / 1.07 km/h
= 11.589 km/h