Figure P5.51 shows the velocity graph of a 2.0 kg object as it moves along the x -axis. What is

step 1 Here, mass is given 2KG and the velocity versus time graph is also given. Suppose this is veloci

Figure P5.51 shows the velocity graph of a 2.0 kg object as...

Figure P5.51 shows the velocity graph of a $2.0 \mathrm{kg}$ object as it moves along the $x$ -axis. What is the net force acting on this object at $t=1$ s? $\mathrm{At} 4 \mathrm{s} ?$ At $7 \mathrm{s} ?$

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Key Concepts

Acceleration Determination

Acceleration is defined as the rate of change of velocity with respect to time. By interpreting the slope of the velocity graph, one can determine the instantaneous acceleration at specific time points, a concept fundamental to kinematics.

Newton's Second Law

Newton's Second Law of Motion, expressed as F = ma, establishes a direct relationship between the net force acting on an object, its mass, and its acceleration. Knowing the object's mass and determining its acceleration from the graph allows for the computation of the net force.

Velocity Graph Interpretation

Understanding a velocity-time graph is key because it visually represents how an object's velocity changes over time. The slope of the graph at any given point indicates the acceleration at that moment, meaning that the graph can be used to determine instantaneous acceleration values.

Instantaneous Net Force Calculation

Combining the concepts of instantaneous acceleration from the velocity graph with Newton's Second Law enables the calculation of the net force acting on the object at specific moments in time. This process involves finding the derivative (slope) of the velocity at the given times and multiplying by the object's mass.

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