The force acts on a 1.7kg object whose initial speed is 0.44m/s and initial position is x = 0.27. Find the speed of the object when it is a the location x = 0.99m?
To find the speed of the object when it is at the location x = 0.99m, we need to use the concept of work-energy theorem.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In mathematical terms, it can be represented as:
Work = ΔKE
Where:
Work is the work done on the object,
ΔKE is the change in kinetic energy.
In this case, we know the initial speed (v_i) of the object is 0.44 m/s. We need to find its final speed (v_f) when it is at the position x = 0.99m.
To solve this problem, we can follow these steps:
Step 1: Calculate the change in position (Δx) using the given initial and final positions: Δx = (0.99m - 0.27m) = 0.72m.
Step 2: Calculate the work done on the object using the formula: Work = Force * Distance.
- The force acting on the object is not given directly, but we can use Newton's second law, F = ma, to find it. Since the mass (m) of the object is given as 1.7kg, we can calculate the force.
- The acceleration (a) can be found using kinematic equation: Δx = v_i * t + (1/2) * a * t^2. Since the initial velocity (v_i) is given as 0.44 m/s and Δx is 0.72m, we can rearrange the equation to solve for acceleration (a).
- Once we have the acceleration (a), we can substitute it back into Newton's second law to find the force (F).
Step 3: Now that we have the force acting on the object, we can calculate the work done using the work formula: Work = Force * Distance. In this case, the distance is Δx = 0.72m.
Step 4: Finally, since the work done is equal to the change in kinetic energy (Work = ΔKE), we can equate the work done to the change in kinetic energy and solve for the final velocity (v_f). The kinetic energy (KE) can be calculated using the formula: KE = (1/2) * m * v^2, where v is the final velocity (v_f).
By following these steps and performing the calculations, we can find the speed of the object when it is at the location x = 0.99m.