Finding Acceleration from Ticker Tape

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

External Link


Interactive Animation