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The position of the object at time t =2.0 s is <u>6.4 m.</u>
Velocity vₓ of a body is the rate at which the position x of the object changes with time.
Therefore,
Write an equation for x.
Substitute the equation for vₓ =2t² in the integral.
Here, the constant of integration is C and it is determined by applying initial conditions.
When t =0, x = 1. 1m
Substitute 2.0s for t.
The position of the particle at t =2.0 s is <u>6.4m</u>
Answer:
-9.46 N
Explanation:
In order to get the value of the x component of the resultant force, we need to get the value of the x component of each force.
This value will be the projection of the force vector, on the x-axis.
For F₁, as it is directed at an angle of 55.0º above the negative x axis, we can find F₁ₓ just applying the definition of cosine of an angle, as follows:
cos θ =
In this case, x = F₁ₓ, and r = F₁
θ, measured from the positive x axis counterclockwise, is as follows:
θ= 180º-55º = 125º
⇒ F₁ₓ = F₁* cosθ = 9.2 N * cos 125º = -5.28 N
We can repeat the process for F₂, as follows:
For F₂, as it is directed at an angle of 53.3º below the negative x axis, we can find F₂ₓ just applying the definition of cosine of an angle, as follows:
cos θ =
In this case, x = F₂ₓ, and r = F₂
θ, measured from the positive x axis counterclockwise, is as follows:
θ= 180º + 53.3º = 233.3º
⇒ F₂ₓ = F₂* cosθ = 7.00 N * cos 233.3º = -4.18 N
The total component of both forces along the x axis, can be found just adding both components, as follows:
Fₓ = F₁ₓ + F₂ₓ = -5.28 N + -4.18 N = -9.46 N