Question

after studying the motion of ball rolling on a straight line as shown in the figure find the displacement and the distance covered when it moves from a to b and then to see and finally comes back to considered as a the reference point.​

Answer 1

Here, the ball starts from A.

Now, first case, it moves from A to B

Then, displacement = length of AB = 10m

And, distance = distance covered by moving from A to B, that is 10 m.

So, in first case, from A to B, distance = displacement = 10m.

Now, in second case, it moves from A to B and then to C.

So, we have, displacement = length of final position - initial position = length of AC.

Now, length of AC = AB - BC

So, length of AC = 10 - 2 = 8 m

Hence, displacement = 8 m

Now, distance = distance actually travelled from A to B and then to C, so it would be 10 + 2 = 12m.

Now, In third case, it moves back to reference point.

So, displacement = Final point - Initial point.

Here, since it moves back to the initial point, it's final point would be the same as initial point.

Hence, here displacement = Final point - final point = 0 m.

And, distance = Length travelled from A to B and then B to A

=> Distance = 10 + 10 = 20m

Answer 2

Complete answer:

After studying the motion of a ball rolling in a straight line as shown in the figure. Find its distance and displacement covered.  

(i) when it rolls from P to Q and then to R (i.e., P to Q to R)

(ii) Finally comes back to P (i.e., P to P)(take, P as a reference point).

Answer:

(i)The distance and displacement traveled by the ball from P→Q→R are 12m and 8m respectively.

(ii) )The distance and displacement traveled by the ball from P→Q→R→P are 20m and 0m respectively.

Explanation:

Given,

The distance between P, and Q is (D) = 10 m.

The distance between R, and Q is (d) = 2 m.

Then the distance between P, and R is (s) = 8 m

To find,

The distance and displacement when:

(i) It rolls from P to Q and then to R.

(ii) Finally comes back to P.

Calculation,

(i) The distance covered by the ball when it rolls from P to Q and then to R is P→Q→R:

D + d = 10m + 2m = 12m. (As distance is scalar, so it is added)

The displacement covered by the ball when it rolls from P to Q and then to R is P→Q→R:

D - d = 10m - 2m = 8m. (As displacement is vector, it is subtracted)

(ii) The distance covered by the ball when it rolls from P to Q to R to P is P→Q→R→P:

D + d + s = 10m + 2m + 8m = 20m.

The displacement covered by the ball when it rolls from P to Q to R to P is P→Q→R→P:

D - d - s = 10m - 2m - 8m = 0m.

Therefore,

(i)The distance and displacement traveled by the ball from P→Q→R are 12m and 8m respectively.

(ii) )The distance and displacement traveled by the ball from P→Q→R→P are 20m and 0m respectively.

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