# Question #5b412

##### 1 Answer

In general velocity is **not** directly proportional to time.

#### Explanation:

Velocity would be directly proportional to time only if the initial velocity (at time **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

- 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