## Description

**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

=0.9320 m/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 v_{i }= initial velocity, V_{o} + ∆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.
- c)

Velocity

Time

e)

Position

Time

- 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.

Velocity 70km/h

37 m/h

4 km/h

0.12h 0.62h

time

- 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