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

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November 11, 2010 at 7:06 AM

ok thanks

March 18, 2014 at 5:01 PM

Why 6 intervals, I dont get it. Help me!

March 18, 2014 at 5:21 PM

6 intervals for the time of acceleration as you have to consider the middle of initial velocity section and the middle of the final velocity section. This will be more accurate. Hope it helps.

February 16, 2017 at 10:01 PM

well the velocity of an accelerating object is always changing at every point, so we take the middle place where it is the average velocity between the two points to make it more accurate.

August 3, 2014 at 1:31 PM

starting from the middle of the first interval?

would that be counted as the first official interval? if so, if counted, there are 7 intervals/vertical slashes made.

August 3, 2014 at 2:35 PM

For finding acceleration it is different. To make it more accurate, the time intervals start and end at the middle of the initial motion and final motion sections.

August 6, 2014 at 6:58 PM

This is correct. You can also use final time minus initial time.

This will give you 7 X 0.02 = 0.14s minus 0.02s = 0.12s.

My question – do you use this “change in time” to calculate accelleration even if the dots were evenly spaced – constant velocity?

August 6, 2014 at 8:10 PM

If it is moving at constant velocity, there will not be acceleration as the initial velocity and final velocity are the same.

October 5, 2014 at 12:58 PM

1/2+ 5 + 1/2 = 6 intervals

August 5, 2015 at 1:21 AM

Thanks.

February 22, 2016 at 8:08 PM

I counted seven intervals…

February 22, 2016 at 8:19 PM

The time for the acceleration starts from the middle of the 2 cm to the middle of the 4 cm. This is to make it more accurate. So there are 6 intervals

March 3, 2016 at 7:07 PM

how do you find the average speed?

March 3, 2016 at 7:28 PM

Take the total distance divided by the time. But count the intervals not the dots to find total time taken.

August 30, 2016 at 4:27 PM

what is the total distance in this case?

September 15, 2016 at 7:26 AM

U can measure the distance from the first to last dot if u need to know the distance travelled by the car. Especially if you are looking for average speed = total distance /total time

For this case you are looking for acceleration.

July 4, 2016 at 1:45 AM

thanks .it had become difficult for me to to calculate acceleration.

January 19, 2017 at 4:40 AM

obra

February 24, 2017 at 3:39 PM

Sorry,i would like to know why taking middle of first interval and middle of last interval will be more accurate? If we take the middle interval,does it mean that the velocity calculated is only true on the middle point ? If it is,could you guys please let me know why ?

February 24, 2017 at 3:49 PM

Sorry,i am also confused that why we dont need to calculate the time before hitting the first dot.I mean that isnt that the ticker timer machine will also need 0.02 second of time interval to hit the first dot on the tape,so before the when the first dot is formed,there is already 0.02s used to produce the first dot? But we are ignoring the 0.02 second when calculating.Does it contain any physics theory?If it does,sincerely asking for the explanation.Thanks a lot ^^

February 24, 2017 at 5:02 PM

When we find the initial speed (velocity) we use the 1st 2 dots. The speed within the 1st 2 dots is increasing. Hence the initial speed is the average in that interval (I.e. like the middle speed). Hence when we consider the initial time for the initial speed before the acceleration, it will be more accurate to consider from the centre of the interval between the 2 dots. Likewise for the final speed and final time. Hope it helps 🙂

February 26, 2017 at 12:50 AM

Oh,I see,it really helps a lot to me ^^ .But what if the velocity between the 1st 2 dots is constant ? Do we still take the middle point’s speed of the interval ? Or can we take the whole interval instead of half interval during our calculation? So we would not have to minus 1 from the total number of ticker tape when calculating the time.Is it correct? Thank you in advance ^^

And can you also help me to explain this question:

Sorry,i am also confused that why we dont need to calculate the time before hitting the first dot.I mean that isnt that the ticker timer machine will also need 0.02 second of time interval to hit the first dot on the tape,so before the when the first dot is formed,there is already 0.02s used to produce the first dot? But we are ignoring the 0.02 second when calculating.Does it contain any physics theory?If it does,sincerely asking for the explanation.Thanks a lot ^^

THANKSSS

February 26, 2017 at 9:33 AM

Hmm I don’t really understand your question. When finding acceleration the method is also the same. If the velocity is constant there is no acceleration and the intervals are the same.

Even if the give the distance between 1st n 3rd point to let u find the initial speed, when find the time interval between initial final and final velocity, u will still take the middle ie. The 2nd dot. Cos it’s between 1st and 3rd dots.

Unless finding the average speed for the car, say they give u the distance from 1st to 10th dot is 20 cm. Then u take distance 10cm divided by time (9 interval x 0.02s)

U can assume the first dot is made as time =0s

August 30, 2017 at 10:19 PM

How do you calculate the period of a ticker timer?

August 30, 2017 at 10:25 PM

If given that the ticker tape timer makes 50 dots in 1 sec, it means that the time take for 1 dot is 1/50 s. That is the period.

August 30, 2017 at 10:26 PM

Or if frequency is given e.g. 50 Hz, then u can use the formula T = 1/freq to find period T

October 13, 2018 at 10:27 AM

Good lesson.A lot has been learnt. Ttanks