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Question: A particle is moving eastward with a velocity of 5 ms<sup>-1</sup>. If in 10 s the velocity changes ...

A particle is moving eastward with a velocity of 5 ms-1. If in 10 s the velocity changes by 5 ms-1 northwards, what is the average acceleration in this time?

A

12 ms−1NW\frac { 1 } { \sqrt { 2 } } \mathrm {~ms} ^ { - 1 } \mathrm { NW }

B

12 ms−1EN\frac { 1 } { 2 } \mathrm {~ms} ^ { - 1 } \mathrm { EN }

C

2 ms−1NW\sqrt { 2 } \mathrm {~ms} ^ { - 1 } \mathrm { NW }

D

22 ms−1NW2 \sqrt { 2 } \mathrm {~ms} ^ { - 1 } \mathrm { NW }

Answer

12 ms−1NW\frac { 1 } { \sqrt { 2 } } \mathrm {~ms} ^ { - 1 } \mathrm { NW }

Explanation

Solution

Change in velocity,

D V→\overrightarrow { \mathrm { V } } = V→\overrightarrow { \mathrm { V } } 2 + (- V→\overrightarrow { \mathrm { V } } 1) = (52 + 52)1/2 NW = 5Ö2 ms-1 NW

Then a→\overrightarrow { \mathrm { a } } av Δ⃗vΔt=5210NW=12\frac { \vec { \Delta } \mathrm { v } } { \Delta \mathrm { t } } = \frac { 5 \sqrt { 2 } } { 10 } \mathrm { NW } = \frac { 1 } { \sqrt { 2 } } ms-2 NW