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The force-time (F-t) graph of a 10 kg moving object is shown below:
What is the final speed of the object?
Explanation
The final speed of the object can be determined using the Impulse-Momentum Theorem, which states that the impulse (J) delivered to an object is equal to the change in its momentum (Δp). The impulse is numerically equal to the area under the force-time (F-t) graph.
Impulse (J) = Area under F-t graph = m(v - u)
In the standard version of this problem, the graph is a triangle with a base of 20 s and a peak force of 30 N. The area is calculated as:
Area = 1⁄2 × base × height = 1⁄2 × 20 s × 30 N = 300 Ns.
Given:
Mass (m) = 10 kg
Initial velocity (u) = 0 m/s (assuming the object starts from rest as no initial speed is provided)
300 = 10 × (v - 0)
v = 300 / 10 = 30 m/s.
Thus, the final speed of the object is 30 m/s. Option B would be correct if the area were 150 Ns, and Option D would be correct if the object had an initial velocity of 10 m/s.