Question #5b412

Velocity would be directly proportional to time only if the initial velocity (at time `0`) were zero and the rate of acceleration was constant.

Example with initial velocity zero and fixed rate of acceleration:
Suppose a ball is dropped from a very high cliff.
Ignoring air resistance and other minor factors:
- the ball has an initial velocity of 0 (at time 0)
- the ball accelerates at a rate of `9.8 m"/"s^2`
- after 1 second, its velocity will be `9.8 m"/"s`
- after 2 seconds, its velocity will be `2xx9.8=19.6 m"/"s`
- and so on.

Example with non-zero initial velocity (but fixed rate of acceleration):
Suppose the ball was thrown towards the ground below the cliff (see above example) with an initial velocity of `20 m"/"s`
because of the acceleration due to gravity:
- after 1 second the ball would have a velocity of `20+9.8 =29.8 m"/"s`
- after 2 seconds the ball would have a velocity of `20+2xx9.8 = 39.8 m"/"s`
Obviously there is no direct proportion, in this case, between the time and the velocity.

One more example:
Think about what happens when you make a typical trip in a car.
Maybe you drive away from your home at some fairly steady velocity; say `40 km"/"hr. You drive like this for`2# hours; your velocity stays constant, but time moves on. Your velocity can not be proportional to time!