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,

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

Interactive Animation

Alfred Low// April 1, 2010 at 1:45 AMwrong answer, shud be -100?

阿进// April 23, 2011 at 5:50 PMyes,i also find it -100,the time taken should be 0.1×4=0.4.Then,-40／0.4,so get the answer -100........

SaraEmyllia// May 15, 2011 at 1:46 AMi'm not understand the calculation

Sheera Hassan/ 김은희// May 15, 2011 at 7:11 AMthe calculation.. got error? I don't get it.

Hana// July 6, 2011 at 1:18 AMhow 2 get the time=0.8s..?

Hana// July 6, 2011 at 1:19 AMhow 2 get the time=0.8s..?

akukaudandia// March 27, 2012 at 4:44 AMi can't understand

Tze Huay Yeap// May 16, 2012 at 2:18 AMi cnt understand d equation..==

Low Peek Yim// February 6, 2013 at 11:52 PMthe t time taken is wrong. is 20tick X 0.02 = 0.4s. not 40ticks X 0.02s.