Acceleration
1.
Jerry is standing in the middle of the room Tom
runs around the corner. Jerry accelerates to 5m/s in 3 s. Calculate the value
of his acceleration.
a = (v-u)/t =
(5-0)/3 = 1.67 ms-2
2.
Tom is just behind Jerry when he runs into a
mouse hole. Tom hits the wall at a speed of 6m/s. He comes to rest in 0.2s.
Calculate the acceleration of Tom’s head. Does the collision kill Tom?
a = (v-u)/t =
(0-6)/0.2 = -30 ms-2 No,
cartoon characters follow the laws of “Wile E Coyote Physics”
3.
At the end of a 215km race Mark accelerates from
18m/s to 21 m/s in 1.2s. Calculate his acceleration.
a = (v-u)/t = (21-18)/1.2
= 2.5 ms-2
4.
Jeremy pushes the pedal to the metal once again.
His reasonably priced car takes 13.6 seconds to accelerate from 13m/s to 47m/s.
Calculate his acceleration.
a = (v-u)/t =
(47-13)/13.6 = 2.5 ms-2
5.
Thomas is puffing along at 25m/s when the signal
ahead turns to red. He applies his brakes and slows to 11m/s in 35s. Calculate
his acceleration.
a = (v-u)/t =
(11-25)/35 = -0.4 ms-2
6.
An oil tanker’s top speed is 6.7 m/s. If it
decelerates at 0.005m/s2. Calculate how long it takes to stop.
a = (v-u)/t
rearranging t =
(v-u)/a
t = (0 – 6.7)/ -
0.005
t = 1340s = 22 min
Distance = t(v-u)/2
= 1340(0-6.7)/2 = 4489m = 4.5km
7.
At take off the Lunar Module had an acceleration
of 3.4 m/s2. The moon’s gravitational field will accelerate objects
at 1.8m/s2. Calculate the velocity of the Eagle 3s after lift off
from Tranquillity Base.
a = (v-u)/t,
rearranging (v-u) =
at,
(v-0) = (3.4 – 1.8)
3
v = 4.8 ms-1
8.
At 11.40pm on the 14th April 1912 the
Titanic was running at 22 knots (11.3 m/s) when it hit an iceberg. It is
popular lore that the iceberg was spotted 37 seconds before the ship hit it. After
the disaster tests were performed on its sister ship the Olympic. At 18 knots
(9.2 m/s) it took 3 min 15 seconds to stop. Calculate the deceleration of The
Olympic.
a = (v-u)/t a= (0-9.2)/(3 x 60) +15, a = -9.2/195 = -0.05 ms-2
Assume the Titanic decelerated at the same
rate, and the officers on the bridge had reacted immediately. Calculate it’s
velocity after 37 seconds of deceleration.
a = (v-u)/t,
rearranging (v-u)= at,
(v – 11.3) = -0.05 x 37,
(v – 11.3) = -1.74,
v = 11.3 – 1.74 =
9.6 ms-2
(The 37 seconds was calculated after the
event. It was the time needed for the Titanic to have swerved away from the
iceberg)
9.
On 16 August 1960, US Air Force Captain Joseph
Kittinger entered the record books when he stepped from the gondola of a helium
balloon floating at an altitude of 31,330 m (102,800 feet) and took the longest
skydive in history. Later he said this
“No wind whistles or billows my clothing. I
have absolutely no sensation of the increasing speed with which I fall. [The
clouds] rushed up so chillingly that I had to remind myself they were vapour
and not solid.”
The density of air at 30 km is roughly 1.5
% that at sea level. Do we need to consider air resistance or drag? At this height air resistance is negligible
At
such extreme altitudes the acceleration due to gravity is not the standard 9.81
m/s2, but the slightly lower value of 9.72 m/s2.
He fell for 28 seconds before deploying a
stabilising parachute. What speed did he reach? Compare this to the speed of
sound (which you will have to look up)
v = u + at {
a = (v-u)/t at = v –u at + u = v }
v = 0 + (9.72 x 28)
v = 272 ms-1 (speed of sound at 00C
= 330ms-1)
