A particle is moving east-wards with a velocity of 5m/s. in 10 seconds the velocity changes to 5 m/s northwards.What is the average acceleration in this time ?

Initial velocity, u = 5 m/s due east

Final velocity, v = 5 m/s due north

Change in velocity, Δv = v – u = 5 m/s due north - 5 m/s due east

=> Δv = 5 m/s due north + 5 m/s due west  [negative of east direction is west]

Δv = (v² + u²)^1/2

=> Δv = 5√2 m/s

Direction of Δv is given by,

tanθ = v/u = -1

=> θ = -45^o

Thus, the acceleration is a = Δv/t =  5√2/10 = 1/√2 m/s² and is directed towards North-West direction.