Question

16 what information can you calculate from this graph? clear all impulse initial velocity final velocity change in mass

Explanation:

Step1: Recall the formula for impulse

Impulse \(J\) is given by the area under the force - time graph. Mathematically, \(J=\int_{t_1}^{t_2}Fdt\). For a force - time graph, if the graph has a simple geometric shape (like a triangle in this case), we can use the formula for the area of the geometric shape. The area of a triangle is \(A = \frac{1}{2}\times base\times height\). In a force - time graph, the base is the time interval and the height is the force value.

Step2: Analyze the other options

• Initial velocity: To find the initial velocity, we would need information about the state of the object before any force (from the graph) acts on it. The force - time graph alone does not give us the initial velocity of the object. We would need additional information like the mass of the object and the relationship \(F = ma\) integrated over time along with initial conditions.
• Final velocity: Similar to the initial velocity, to find the final velocity, we need the mass of the object (since \(J=\Delta p=m\Delta v\), where \(p\) is momentum). The force - time graph gives us \(J\), but without the mass \(m\), we cannot calculate \(v_f\) from \(J = m(v_f - v_i)\) (where \(v_i\) is also unknown without more data).
• Change in mass: The force - time graph is related to the motion of an object (through \(F=ma\) and \(J=\Delta p\)). There is no direct relationship in classical mechanics (where \(F - t\) graphs are typically used in basic problems) between force - time and change in mass. The formula \(F=\frac{dp}{dt}=\frac{d(mv)}{dt}=m\frac{dv}{dt}+v\frac{dm}{dt}\) would require information about velocity and its derivative to find \(\frac{dm}{dt}\), which is not available from a simple \(F - t\) graph.

Answer:

Impulse