Answer:

Introduction:
The change in velocity of a truck travelling due North at 20 metre per second and turning East at the same speed can be calculated by using the concept of vector addition and trigonometry.

Vector Addition:
When the truck turns East, its velocity changes because it is now moving in a different direction. The new velocity can be found by adding the North and East components of the velocity vectors.

Trigonometry:
Using trigonometry, we can find the North and East components of the velocity vectors. If we assume that the truck turned at a right angle, then the East component of the velocity will be equal to the North component.

Calculation:
The velocity vector of the truck travelling due North is given by:
$v_{N} = 20 \hat{j}$

The velocity vector of the truck travelling East is given by:
$v_{E} = 20 \hat{i}$

The change in velocity can be found by adding the North and East components of the velocity vectors:
$\Delta v = v_{E} + v_{N} = 20 \hat{i} + 20 \hat{j}$

The magnitude of the change in velocity can be found using the Pythagorean theorem:
$|\Delta v| = \sqrt{(20)^2 + (20)^2} = 28.28$ m/s

The direction of the change in velocity can be found using trigonometry:
$\theta = \tan^{-1}\left(\frac{20}{20}\right) = 45^{\circ}$ East of North

Conclusion:
The change in velocity of the truck travelling due North at 20 metre per second and turning East at the same speed is 28.28 m/s at 45 degrees East of North.