Tara embarked on a camel safari in Africa. She traveled 5 km north, then 3 km east, and finally 1 km north again. What total distance did she cover? What was her displacement?

Total distance covered: The total distance covered is simply the sum of all the distances Tara traveled in each direction, irrespective of the direction.

So, Tara traveled: 5 km north + 3 km east + 1 km north = 5 km + 3 km + 1 km = 9 km.

Therefore, the total distance Tara covered during her camel safari is 9 km.

Displacement: Displacement, on the other hand, is a vector quantity that refers to how far out of place an object is; it is the object's overall change in position. Displacement has both magnitude and direction. To find Tara's displacement, we need to consider the initial and final position and the straight line between them.

We can construct a right-angled triangle with the legs representing the northward and eastward components of Tara's journey, and the hypotenuse representing the displacement.

Northward travel: 5 km + 1 km = 6 km Eastward travel: 3 km

Now, using the Pythagorean theorem for the right-angled triangle:

Displacement^2 = Northward travel^2 + Eastward travel^2 Displacement^2 = (6 km)^2 + (3 km)^2 Displacement^2 = 36 km^2 + 9 km^2 Displacement^2 = 45 km^2 Displacement = √(45 km^2) Displacement = √(45) km Displacement ≈ 6.7 km

The exact value for the square root of 45 is a little bit cumbersome to work with without a calculator, so we can leave it in the square root form for an exact value or calculate an approximate value, which in this case is about 6.7 kilometers.

As for the direction, since Tara has traveled north and east, her displacement is in the northeast direction.

So Tara's displacement is approximately 6.7 km in the northeast direction.