Question

If the area under the graph between the force on an object and time is 20 units, then the object experiences

• A. an impulse of 10 units
• B. a change of momentum of 10 units
• C. an impulse of 20 units
• D. a change of force by 20 units
• E. a change of acceleration of 20 units

Hint:

Logic Tip: Always check the axes of a graph to determine what the area or slope represents. Area = (y-axis unit) $\times$ (x-axis unit). Here, Newton $\times$ seconds = N$\cdot$s, which is the standard unit for both Impulse and Momentum.

Answer 1

The Correct Option is C

Concept:
In physics, the area under a Force-Time ($F-t$) graph represents the mathematical integral of force with respect to time ($\int F , dt$). By definition, the integral of force over a time interval is equal to the **Impulse** ($J$) applied to the object. Furthermore, according to the Impulse-Momentum Theorem, Impulse is exactly equal to the change in momentum ($\Delta p$).
Step 1: Relate the graph area to the physical quantity.
$$\text{Area} = \int F , dt = \text{Impulse } (J)$$
Step 2: Evaluate the given data.
We are given that the area under the graph is 20 units. Therefore: $$\text{Impulse} = 20\text{ units}$$ $$\text{Change in Momentum} = 20\text{ units}$$
Step 3: Compare with the given options.
Option A: Impulse of 10 units (Incorrect, value is wrong). Option B: Change of momentum of 10 units (Incorrect, value is wrong). Option C: Impulse of 20 units (Correct). Option D \& E: Incorrect physical quantities.