Question

An object, which is at the origin at time t=0

Answer 1

At time t=0, an object at the origin has a constant acceleration a=(6.0i + 3.0j)m/s2 and an initial velocity V0= (-14.0i - 7.0j)m/s (-16.3 I - 8.2 j) The position x at which the object comes to rest is denoted by m. (temporarily).

What exactly is Origin?

A body's origin of motion is defined as the point at which a body or object begins to move.

• The act of being born, existing, or beginning; point of departure.
• That causes something to happen.
• That which serves as a source or is derived from something.
• In the field of coordinate geometry, the origin is defined as the initial point or starting point from which we begin our calculations or measurements. We start at zero on a ruler.
• Because the 0 on a ruler is where we start measuring, it is referred to as the scale's origin.
• The center of a coordinate axis is defined as coordinate 0 in all axes.

Hence, at time t=0, an object at the origin has an initial velocity V0 of (-14.0i - 7.0j)m/s and a constant acceleration an of (6.0i + 3.0j)m/s2. r = (-16.3 I - 8.2 j) m is the position x at which the object comes to rest (temporarily).

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Answer 2

An object, which is at the origin at time t=0, has initial velocity V₀= (-14.0i - 7.0j)m/s and constant acceleration a=(6.0i + 3.0j)m/s². The position x where the object comes to rest (momentarily) is, r = ( -16.3 i - 8.2 j ) m

What is position?

Position is a term that means a object where placed. In other words a object is placed or stayed or comes to rest that place called the position of the object.

How can we calculate the position?

To calculate the position of the object we are using two formulas, like

V= V₀+∫a dt

r=r₀+∫v dt

Here we are given,

V₀=initial velocity of the object=(-14.0i - 7.0j)m/s,

a=constant acceleration of the object= (6.0i + 3.0j)m/s²

Now we put the values in the first formula,

V= V₀+∫a dt

Or, V= (-14.0i - 7.0j)+ ∫(6.0i + 3.0j) dt

Or, V= (-14.0+6.0t)i + (- 7.0+ 3.0t)j

According to the question, the particle becomes rest then,

V(x)=0

Or, (-14.0+6.0t)=0

Or, t=7/3S

In other way, V(y)=0

Or, (- 7.0+ 3.0t)=0

Or, t=7/3S

Now we put the value of velocity in the second equation,

r=r₀+∫v dt

Or, r=0+∫(-14.0+6.0t)i + (- 7.0+ 3.0t)j dt

Or, r= (-14.0t+6.0t²)i + (- 7.0t+ 3.0t²)j

Now we put,  t=7/3S, then the r value becomes,

r= (-14.0(7/3)+6.0(7/3)²)i + (- 7.0(7/3)+ 3.0(7/3)²)j

r≈(-16.3 i - 8.2 j)m

From the above calculation we can conclude that, The position x where the object comes to rest (momentarily) is, r = ( -16.3 i - 8.2 j ) m

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