Physics Classroom Kinematics Practice
Michael Matias
September 19th, 2012
1.
An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground.
Determine the distance traveled before takeoff.
d= v_i*t+1/2*a*t^2→d=0+1.6*(32.8)^2→d= 1721m
2.
A car starts from rest and accelerates uniformly over a time
of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
d= v_i*t+1/2*a*t^2→110=0+1/2*a*(5.21)^2→110=13.57a→a=8.1m/s^2
3.
Upton Chuck is riding the Giant Drop at Great America. If
Upton free falls for 2.6 seconds, what will be his final velocity and how far
will he fall?
v_f=v_i+a*t→v_f=0-9.8*2.6→v_f=-25.48m/s
d=(v_i+v_f)/2*t→d=(-25.48)/2*2.6→d=-33.1m
4. A race car accelerates uniformly from 18.5 m/s to
46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the
distance traveled.
v_f=v_i+a*t→46.1=18.5+a*2.47→27.6=2.47a→11.17m/s^2
d=(v_i+v_f)/2*t→d=(18.5+46.1)/2*2.47→d=79.79m
5. A feather is dropped on the moon from a height of
1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to
the surface of the moon.
d= v_i*t+1/2*a*t^2→1.4=0+.8*t^2→t^2=1.75→t=1.32s
6. Rocket-powered sleds are used to test the human
response to acceleration. If a rocket-powered sled is accelerated to a speed of
444 m/s in 1.8 seconds, then what is the acceleration and what is the distance
that the sled travels?
v_f=v_i+a*t→444=1.8*a→a=246.67m/s^2
d=(v_i+v_f)/2*t→d=444/2*1.8→d=399.6m
7. A bike accelerates uniformly from rest to a speed
of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike.
d=(v_i+v_f)/2*t→35.4=3.55t→t=9.97s
v_f=v_i+a*t→7.71=0+9.97*a→a=.77m/s^2
8. An engineer is designing the runway for an
airport. Of the planes that will use the airport, the lowest acceleration rate
is likely to be 3 m/s2. The takeoff speed
for this plane will be 65 m/s. Assuming this minimum acceleration, what is the
minimum allowed length for the runway?
v_f^2=v_i^2+2ad→〖65〗^2=0+2*3*d→4225=6d→d=704.2m
9. A car traveling at 22.4 m/s skids to a stop in
2.55 s. Determine the skidding distance of the car (assume uniform
acceleration).
d=(v_i+v_f)/2*t→d=22.4/2*2.55→d=28.56m
10. A kangaroo is capable of jumping to a height of
2.62 m. Determine the takeoff speed of the kangaroo.
v_f^2=v_i^2+2ad→0=v_i^2+2*-9.8*2.62→v_i^2=51.352→v_i=7.2m/s
11. If Michael Jordan has a vertical leap of 1.29 m,
then what is his takeoff speed and his hang time (total time to move upwards to
the peak and then return to the ground)?
v_f^2=v_i^2+2ad→0=v_i^2+2*-9.8*1.29→v_i^2=25.284→v_i=5.03m/s
Time to peak -> d=(v_i+v_f)/2*t→1.29=5.03/2*t→t=.51s
Hang Time =
2*.51 = 1.02s
12. A bullet leaves a rifle with a muzzle velocity of
521 m/s. While accelerating through the barrel of the rifle, the bullet moves a
distance of 0.840 m. Determine the acceleration of the bullet (assume a uniform
acceleration).
v_f^2=v_i^2+2ad→〖521〗^2=0+2*a*0.84→a=161572m/s^2
13. A baseball is popped straight up into the air and
has a hang-time of 6.25 s. Determine the height to which the ball rises before
it reaches its peak. (Hint: the time to rise to the peak is one-half the total
hang-time.)
v_f=v_i+a*t→0=v_i-9.8*3.125→v_i=30.625m/s
d=(v_i+v_f)/2*t→d=30.625/2*3.125→d=47.9m
14. The observation deck of tall skyscraper 370 m
above the street. Determine the time required for a penny to free fall from the
deck to the street below.
d= v_i*t+1/2*a*t^2→370=0+1/2*9.8*t^2→370=4.8t^2→t=8.78s
15. A bullet is moving at a speed of 367 m/s when it
embeds into a lump of moist clay. The bullet penetrates for a distance of
0.0621 m. Determine the acceleration of the bullet while moving into the clay.
(Assume a uniform acceleration.)
v_f^2=v_i^2+2ad→0=〖367〗^2+2*a*.0621→0=134689+0.1242a→a=-1084452m/s^2
16. A stone is dropped into a deep well and is heard
to hit the water 3.41 s after being dropped. Determine the depth of the well.
d= v_i*t+1/2*a*t^2→d=0+1/2*-9.8*〖3.41〗^2→d=-57m
17. It was once recorded that a Jaguar left skid
marks that were 290 m in length. Assuming that the Jaguar skidded to a stop
with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it
began to skid.
v_f^2=v_i^2+2ad→0=v_i^2+2*-3.9*290→v_i^2=2262→v_i^2=47.6m/s
18. A plane has a takeoff speed of 88.3 m/s and
requires 1365 m to reach that speed. Determine the acceleration of the plane
and the time required to reach this speed.
v_f^2=v_i^2+2ad→〖88.3〗^2=0+2*a*1365→a=2.86m/s^2
d=(v_i+v_f)/2*t→1365=88.3/2*t→t=30.92s
19. A dragster accelerates to a speed of 112 m/s over
a distance of 398 m. Determine the acceleration (assume uniform) of the
dragster.
v_f^2=v_i^2+2ad→〖112〗^2=0+2*a*398→a=15.76m/s^2
20. With what speed in miles/hr (1 m/s = 2.23 mi/hr)
must an object be thrown to reach a height of 91.5 m (equivalent to one
football field)? Assume negligible air resistance.
v_f^2=v_i^2+2ad→0=v_i^2+2*-9.8*91.5→v_i^2=42.4m/s=94.6mi/hr
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