Question

A particle is moving with velocity 5 m/s towards east and its velocity changes to 5 m/s north in 10 sec. Find the acceleration.
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EN-W
(2
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V2
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Answer 1

Answer:

North (y direction)

                   ^

                   |

                   |

West <===========> east  (x direction)

Initial velocity = 5 m/sec  i                   i = unit vector along x

Final velocity = 5 m/sec  j                    j = unit vector along y

Change of velocity =  final - initial = 5 j - 5 i m/sec = 5 (j-i) m/sec

Resultant vector of the two vectors: j, and -i is =

[tex] Magnitude = \sqrt{ 5^2 + 5^2 } = 5 \sqrt{2} m/sec

Acceleration = change of velocity / time duration

      = 5 (j - i) /10 m/sec²   = 1/2 * (j - i) m/sec² .

It s magnitude = √(1²+(-1)²) / 2 = √2/2 = 1 / √2 m/sec²

Its direction is given by tan Ф = 1 * sin 90 / [ 1 - 1 cos 90 ] = 1

            So Ф = 45 deg.

It is 45 deg in counter clock wise direction from y axis.  It means North-West direction.

Explanation: