2.4. Uniform Acceleration http://www.ck12.org
As common as the term acceleration is, there is a good deal of confusion surrounding the concept. An object can
have any acceleration and simultaneously have a zero velocity. The velocity of an object at any instant (think of the
speedometer in your car) gives no information in determining the object’s acceleration, only therate of changeof
velocity can be used to determine the object’s acceleration.
Thinking About Acceleration
Suppose that a cheetah, starting from rest, has an acceleration of over 33 (km/hr/s), or kilometers per hour per
second. After one second, the cheetah has a speed of 33 km/h, after two seconds, its speed is 66 km/h, and after
three seconds, its speed is 99 km/h and 99 km/h is over 60 mph. So it takes a cheetah only three seconds to “go from
zero to 60.”
The cheetah increases its velocity by 33 km/h every second. The units help to explain that acceleration depends upon
the changing rate of velocity. 33 km/h is the same as 9.2 m/s (meters per second). So an acceleration of 33 km/h
per second is 9.2 m/s per second. This is expressed as 9.2 m/s^2. Using dimensional analysis, we can see this from
the formula for acceleration,a=∆∆vt=
(m
s)( 1
s)
=ms 2.FIGURE 2.13
The cheetah is the fastest land animal.Check Your Understanding
- Thompson’s gazelle can reach a speed of 65 km/h in four seconds. What is its acceleration in km/h/s and m/s^2?
Answer:A useful conversion to remember is 1 km/h= 185 m/s.
(1 km/h)×
(1000 m
1 km)
×
( 1 h
3600 s)
= 185 m/sUsing this conversion, 65 km/h = 18 m/s, the acceleration is:a=∆∆vt=18 m/s4 s = 4 .5 m/s^2.
- A Thompson’s gazelle has a maximum acceleration of 4.5 m/s^2. At this acceleration, how much time is required
for it to reach a speed of 40 km/h?
Answer:Using our conversion from before, 1 km/h= 185 m/s, we can make a conversion fraction for km/h to m/s.
40 km/h×
185 m/s
1 km/h=11 m/s
If the gazelle started from rest, and accelerates at 4.5m/s^2 , then after the first second its speed is 4.5 m/s, after the
second second, its speed is 9.0 m/s, and after the third second its speed is 13.5 m/s. So we know the answer must be