ticker timer traces

Displacement - time graphs

Acceleration due to gravity

If you only have a small strip of tape then cut along the dots.  Each dot was produced 1/50 s after the one before it.
This means the tape's velocity (and the velocity of the falling weight)
= (distance of tape in m) / (1/50)

If you measure the distance (x) in cm then v = (x/100) / (1/50) = (x/100) x 50 = 0.5x

What to do

Measure the distance of the first strip you have in cm. Divide this by 2 to get the velocity in m/s

Measure the distance of the last strip you have in cm. Divide this by 2 to get the velocity in m/s

work out the velocity change.

Count the nuber of strips you have. Each strip represents 1/50s. So the time taken for the velocty change you have calculated is (number of strips /50) s.

Now divide the velocty change calculated by the number of strips. Multiply your answer by 50 to ge the acceleration.

To work

Acceleration

Answers to acceleration calculations

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 14^th 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)