The diagram shows a strip of paper tape that has been pulled under a vibrating arm by a car moving to the left. The arm is vibrating regularly, making 50 dots per second. What was the acceleration of the car?

Solutions: View the video tutorial to understand where to take time interval.

The arm vibrating **50 dots per second = frequency of 50 Hz** (50 holes are produced in 1 second)

Hence, the period, T = 1/f = 1 / 50 = 0.02s * (every 0.02s, a hole is created on the tape)*

To find acceleration, a, we need to find **initial velocity, u**,and the **final velocity, v**.

u = dist / time = 0.02m/0.02s = 1 m/s

v = dist / time = 0.04m/0.02s = 2 m/s

To find acceleration, we can use a = (v-u)/t , but the time, t, taken for the increase in velocity is where most students will make a mistake.

Many will take 7 intervals to calculate the t, which is wrong.

But the intervals should be** 6, starting from the middle of first interval and middle of last interval**.

This will give a more accurate acceleration.

Hence, t = 6 x 0.02s = 0.12s a = (v-u)/t = (2-1)/0.12 = 8.33 m/s2