Question #5b412

1 Answer
Mar 13, 2017

In general velocity is not directly proportional to time.


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!