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:

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,
$$u=\frac{s}{t}=\frac{3cm}{0.02s}=150cm{s}^{-1}$$
Final velocity,
$$v=\frac{s}{t}=\frac{0.5cm}{0.02s}=25cm{s}^{-1}$$
Time taken for the velocity change,
t = (0.5 + 4 + 0.5) ticks = 5 ticks
t = 5 × 0.02s = 0.1s

Acceleration,
$$\begin{array}{l}a=\frac{v-u}{t}\\ a=\frac{25-150}{0.1}=-1250cm{s}^{-1}\end{array}$$

Example:

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,
$$u=\frac{s}{t}=\frac{5cm}{0.1s}=50cm{s}^{-1}$$ Final velocity
$$v=\frac{s}{t}=\frac{1cm}{0.1s}=10cm{s}^{-1}$$ Time taken for the velocity change,
t = (2.5 + 5 + 5 + 5 + 2.5) ticks = 20 ticks
t = 20 × 0.02s = 0.4s

Acceleration,
$$\begin{array}{l}a=\frac{v-u}{t}\\ a=\frac{10-50}{0.4}=-100cm{s}^{-1}\end{array}$$
Video below shows the step by step solution to this problem.

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