In general velocity is not directly proportional to time.
Velocity would be directly proportional to time only if the initial velocity (at time
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
- after 1 second, its velocity will be
- after 2 seconds, its velocity will be
- 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
because of the acceleration due to gravity:
- after 1 second the ball would have a velocity of
- after 2 seconds the ball would have a velocity of
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