Finding Acceleration

Acceleration of a motion can be determined by using ticker tape through the following equation:

Caution!:
t is time taken from the initial velocity to the final velocity.


Example 1

The ticker-tape in figure above was produced by a toy car moving down a tilted runway. If the ticker-tape timer produced 50 dots per second, find the acceleration of the toy car.

Answer:

In order to find the acceleration, we need to determine the initial velocity, the final velocity and the time taken for the velocity change.

Initial velocity,

\[ u = \frac{s}{t} = \frac{{3cm}}{{0.02s}} = 150cms^{ - 1}\]

\[ v = \frac{s}{t} = \frac{{0.5cm}}{{0.02s}} = 25cms^{ - 1}\]


Time taken for the velocity change,
t = (0.5 + 4 + 0.5) ticks = 5 ticks
t = 5 × 0.02s = 0.1s

Acceleration,
\[a = \frac{{v - u}}{t} = \frac{{25 - 150}}{{0.1}} = - 1250cms^{ - 1}\]

Example 2

A trolley is pushed up a slope. Diagram above shows ticker tape chart that show the movement of the trolley. Every section of the tape contains 5 ticks. If the ticker-tape timer produced 50 dots per second, determine the acceleration of the trolley.

Answer:

In order to find the acceleration, we need to determine the initial velocity, the final velocity and the time taken for the velocity change.

Initial velocity,
\[ u = \frac{s}{t} = \frac{{5cm}}{{5 × 0.02s}} = 50cms^{ - 1}\]

\[ v = \frac{s}{t} = \frac{{1cm}}{{5 × 0.02s}} = 10cms^{ - 1}\]


Time taken for the velocity change,
t = (2.5 + 5 + 5 + 5 + 2.5) ticks = 40 ticks
t = 40 × 0.02s = 0.8s

Acceleration,
\[a = \frac{{v - u}}{t} = \frac{{10 - 50}}{{0.8}} = - 50cms^{ - 1}\]


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9 comments

  1. Alfred Low // April 1, 2010 at 1:45 AM  

    wrong answer, shud be -100?

  2. 阿进 // April 23, 2011 at 5:50 PM  

    yes,i also find it -100,the time taken should be 0.1×4=0.4.Then,-40/0.4,so get the answer -100........

  3. SaraEmyllia // May 15, 2011 at 1:46 AM  

    i'm not understand the calculation

  4. Sheera Hassan/ 김은희 // May 15, 2011 at 7:11 AM  

    the calculation.. got error? I don't get it.

  5. Hana // July 6, 2011 at 1:18 AM  

    how 2 get the time=0.8s..?

  6. Hana // July 6, 2011 at 1:19 AM  

    how 2 get the time=0.8s..?

  7. akukaudandia // March 27, 2012 at 4:44 AM  

    i can't understand

  8. Tze Huay Yeap // May 16, 2012 at 2:18 AM  

    i cnt understand d equation..==

  9. Low Peek Yim // February 6, 2013 at 11:52 PM  

    the t time taken is wrong. is 20tick X 0.02 = 0.4s. not 40ticks X 0.02s.