Acceleration
In everyday, the word acceleration is often used
to describe a state of increasing speed. For many Americans, their only
experience with acceleration comes from car ads. When a commercial shouts
"zero to sixty in six point seven seconds" what they're saying here
is that this particular car takes 6.7 s to reach a speed of 60 mph
starting from a complete stop. This example illustrates acceleration as it is
commonly understood, but acceleration in physics is much more than just
increasing speed.
In Physics Acceleration is the rate of change of velocity
with time. These means that any changes
in the velocity of an object results in acceleration: increasing speed,
decreasing speed (also called deceleration) or changing direction. Thus, a falling apple accelerates, a car stopping at a traffic
light accelerates, and an orbiting planet accelerates. Acceleration occurs
anytime an object's speed increases, decreases, or changes direction.
Average acceleration is determined over a "long" time
interval. The word long in this context means finite — something with a
beginning and an end. The velocity at the beginning of this interval is called
the initial velocity (vi) and the velocity at the end is called the final velocity (vf). Average acceleration is a quantity calculated
from measurements.
where
a represents acceleration
vf represents the final velocity of the object
vi represents the initial velocity of the object
t represents the time that takes change the
velocity.
Units
Calculating acceleration involves dividing
velocity by time — or in terms of units, dividing meters per second [m/s] by
second [s]. Dividing distance by time twice is the same as dividing distance by
the square of time. Thus the SI unit of acceleration is the meter per second squared (m/s2)
of kilometers per hour squared (km/h2)
Now you have some problems
to solve, remember uses the algorism for solve problems. In some cases you will
need to clearway the formula or use the triangle.
1.
A
helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the
acceleration of this helicopter?
2.
As
she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds.
What is her deceleration?
3.
After
traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the
runner’s acceleration?
4.
A
car accelerates at a rate of 3.0 m/s2. If its original
speed is 8.0 m/s, how many seconds will it take the car to reach a final speed
of 25.0 m/s?
5.
A
motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s2 for 6.0 seconds. What is the final speed of the
motorcycle?
6. A
roller coaster car rapidly picks up speed as it rolls down a slope. As it
starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom
of the slope, its speed is 22 m/s. What is its average acceleration?
7. A
cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration?
Is this acceleration higher than that of a car which accelerates from 0 to 30
m/s in 8 seconds?
8. A
car advertisement states that a certain car can accelerate from rest to 70 km/h
in 7 seconds. Find the car’s average acceleration.
9. A
lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard’s
average acceleration?
10. A runner covers the
last straight stretch of a race in 4 s. During that time, he speeds up from 5
m/s to 9 m/s. What is the runner’s acceleration in this part of the race?
11. You are traveling in
a car that is moving at a velocity of 20 m/s. Suddenly, a car 10 meters in
front of you slams on it’s brakes. At that moment, you also slam on your brakes
and slow to 5 m/s. Calculate the acceleration if it took 2 seconds to slow your
car down.
12. A ball is dropped
from the top of a building. After 2 seconds, its velocity is measured to be
19.6 m/s. Calculate the acceleration for the dropped ball.
13. A car starting from rest accelerates
at a rate of 8.0 m/s/s. What is its final speed at the end of 4.0 seconds?
14. A cyclist accelerates at a rate of 7.0
m/s2. How long will it take the cyclist to reach a
speed of 18 m/s?
15. A skateboarder traveling at 7.0 meters
per second rolls to a stop at the top of a ramp in 3.0 seconds. What is the
skateboarder’s acceleration?
16. If a Ferrari, with an
initial velocity of 10 m/s, accelerates at a rate of 50 m/s/s for 3 seconds,
what will its final velocity be?
17. Falling objects drop
with an average acceleration of 9.8 m/s2. If an object falls from a tall
building, how long will it take before it reaches a speed of 49 m/s?
18. Josh rolled a bowling
ball down a lane in 2.5 s. The ball traveled at a constant acceleration of 1.8
m/s2 down the lane and was traveling at a speed of 7.6 m/s by the time it
reached the pins at the end of the lane. How fast was the ball going when it
left Tim’s hand?