# calculating acceleration from velocity and time

## calculating average acceleration in one direction

Calculating acceleration is complicated if both speed and direction are changing or if you want to know acceleration at any given instant in time. However, its relatively easy to calculate average acceleration over a period of time when only speed is changing. Then acceleration is the change in velocity (represented by v) divided by the change in time (represented by t): acceleration = v t

## accelerating on a bike

Look at the cyclist in the Figure 1.1. With the help of gravity, he speeds up as he goes downhill on a straight part of the trail. His velocity changes from 1 meter per second at the top of the hill to 6 meters per second by the time he reaches the bottom. If it takes him 5 seconds to reach the bottom, what is his average acceleration as he races down the hill? v t 6 m/s 1 m/s = 5s 5 m/s = 5s 1 m/s = 1s = 1 m/s2 acceleration = In words, this means that for each second the cyclist travels downhill, his velocity (in this case, his speed) increases by 1 meter per second on average. Note that the answer to this problem is expressed in m/s2 , which is the SI unit for acceleration. Q: The cyclist slows down at the end of the race. His velocity changes from 6 m/s to 2 m/s during a period of 4 seconds without any change in direction. What was his average acceleration during these 4 seconds? A: Use the equation given above for acceleration: v t 6 m/s 2 m/s = 4s 4 m/s = 4s 1 m/s = 1s = 1 m/s2 acceleration =

## instructional diagrams

No diagram descriptions associated with this lesson

## questions

which equation is used to calculate average acceleration when only speed is changing?

``````-->  a) average acceleration = v/t

b) average acceleration = t/v

c) average acceleration = d/t

d) average acceleration = v/t
``````

it is easier to calculate acceleration for any given moment of time than to calculate average acceleration for a period of time.

``````a. true

-->  b. false
``````

the si unit for acceleration is

``````a) m/s.

b) m/s2.

-->  c) m/s2.

d) none of the above
``````

which of the following units could represent acceleration?

``````a) cm/s

-->  b) km/h2

c) m/h

d) cm/h
``````

## diagram questions

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