Question

The figure shows a velocity-versus-time graph for a particle moving along the x-axis. At t=0s, assume that x=0m. What is the particle's position at t=3.0s?

Answer 1

Using the velocity-time graph, the displacement can be calculated by the area under the velocity-time graph. At 3 seconds the total displacement is then equal to (4)(2) + (4 + 2)*1/2 = 11 m. Assuming that the starting point is at x = 0, then the particle at t=3s is at x=11 m.


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Answer 2

The particle's position at 3 seconds is equal to 11 meters.

What is a particle's position?

The position of a particle that is moving in a straight line is considered to be a vector quantity, which represents a point (P) on the straight line with respect to the origin (O).

Basically, a particle's position is a function of time and it is usually written as x(t).

How to calculate a particle's position.

In order to calculate a particle's position or the displacement of this particle, we would determine the area of the velocity-versus-time graph.

Mathematically, the displacement of the particle is equal to the sum of the area of rectangle and the area of a trapezium.

$Displacement = ab + (\frac{a+b}{2} \times 1)\\\\Displacement = 4 \times 2 + (\frac{4+2}{2} \times 1)\\\\Displacement =8+3$

Displacement = 11 meters.

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