Suppose the position of an object is given by a vector

In summary, the position of an object is given by r⃗ = (3.0t2i^ - 6.0t3j^)m and we are asked to find r⃗ at time t = 2.5 s. By plugging in 2.5 seconds to the r equation, we get the answer of 19i-73j, expressed in terms of the unit vectors i^ and j^. However, when inputting this answer into the homework, it was marked as incorrect. After trying different variations, it was discovered that the correct answer is 18.75i-73.002j, expressed using two significant figures.
  • #1
sunnyday
6
0

Homework Statement


Suppose the position of an object is given by r⃗ = (3.0t2i^ - 6.0t3j^)m. Where t in seconds.

Determine r⃗ at time t = 2.5 s. Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^.

Homework Equations


plugging in 2.5 seconds to the r equation

The Attempt at a Solution


r = 3(2.5)^2i-6(2.5)^3j -> 18.75i-73.002j -> 19i-73j

When I put this answer in my homework, it says it's wrong. I even tried (19i-73j) and it says it's wrong.
 
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  • #2
sunnyday said:
6(2.5)^3
Yes.
sunnyday said:
73.002
No.
 
  • Like
Likes sunnyday
  • #3
haruspex said:
Yes.

No.
oh what. nvm. that was so weird. thank u so much!
 

Related to Suppose the position of an object is given by a vector

1. What is a vector?

A vector is a quantity that has both magnitude and direction. It is represented by an arrow with a length and direction, where the length represents the magnitude and the direction represents the direction of the vector.

2. How is the position of an object described by a vector?

The position of an object is described by a vector by using a reference point and specifying the distance and direction from that point to the object's location. This creates a displacement vector that represents the position of the object.

3. Can a vector change over time?

Yes, a vector can change over time. This is known as a changing or time-varying vector. It can change in magnitude, direction, or both, depending on the movement of the object it represents.

4. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. For example, if the vector is represented by (x,y), the magnitude would be √(x² + y²).

5. What is the difference between a displacement vector and a position vector?

A displacement vector represents the distance and direction between two points, while a position vector represents the location of a point relative to a reference point. In other words, a displacement vector shows how an object has moved, while a position vector shows where the object is located.

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