Question 5b412

Mar 13, 2017

In general velocity is not directly proportional to time.

Explanation:

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 $9.8 m \text{/} {s}^{2}$
- after 1 second, its velocity will be $9.8 m \text{/} s$
- after 2 seconds, its velocity will be $2 \times 9.8 = 19.6 m \text{/} s$
- 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 $20 m \text{/} s$
because of the acceleration due to gravity:
- after 1 second the ball would have a velocity of $20 + 9.8 = 29.8 m \text{/} s$
- after 2 seconds the ball would have a velocity of $20 + 2 \times 9.8 = 39.8 m \text{/} s$
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 k m \text{/} h r . Y o u \mathrm{dr} i v e l i k e t h i s f \mathmr{and}$2 hours; your velocity stays constant, but time moves on. Your velocity can not be proportional to time!