Calculating the magnitude of displacement

In summary, the car's displacement can be calculated by finding the difference between the East and West vectors and using the Pythagorean theorem to find the resultant vector. The magnitude of the displacement is approximately 13km, not 17km as originally calculated. This is because the Pythagorean theorem takes into account the direction of the displacement, not just the distance traveled.
  • #1
microlab
2
0
A car us driven at a velocity of 72km/h EAST for 0.50hr, 48km/h NORTH for 0.25hr, and 62km/h WEST for 0.50hr. Calculate the magnitude of its displacement.

Attempt at the solution:

Distance = Speed * Time

(72 x 0.5) + (48 x 0.25) - (62 x 0.5) = 17km

However, the answer in the book says 13km and I can't figure out how..
 
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  • #2
If you go 1 km north and 1 km east, you're not 2 km away from where you started; you're about 1.4 km away. This is the quantity you're being asked for. What do you know about the pythagorean theorem?
 
  • #3
Oh okay, I get it.. So i have to get the difference of the East and West vectors and use pythagorean theorem to find the resultant vector.
 

FAQ: Calculating the magnitude of displacement

What is displacement?

Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position.

How is displacement calculated?

To calculate displacement, you need to find the difference between the initial and final position of an object. This can be calculated using the formula: displacement = final position - initial position. Displacement is typically measured in units of distance, such as meters or kilometers.

What is the difference between displacement and distance?

While both displacement and distance are measures of an object's movement, they differ in that displacement takes into account the direction of movement, while distance simply measures the total amount of ground covered by the object.

Can displacement be negative?

Yes, displacement can be negative. This occurs when an object moves in the opposite direction of its initial position. For example, if an object starts at position 5 and moves to position 2, its displacement is -3 units.

How is displacement represented?

Displacement can be represented using a vector, which includes both magnitude (distance) and direction. It can also be represented using a graph, with the initial and final positions marked and the displacement shown as an arrow connecting the two points.

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