The figure displays the graph of the x -coordinate of a particle travelling along the X-axis as a function of time. Determine the instantaneous velocity of the particle at 2 s , 5 s , 8 s , and 12 s respectively.

Step-by-step solution

The instantaneous velocity of a particle is given by the slope of its position-time ( x-t ) graph, v = dx dt . At t = 2 s , the particle is on the line segment from t = 0 to t = 2.5 s . The slope is: v₁ = 50 - 0 2.5 - 0 = 20 m/s At t = 5 s , the particle is on the horizontal line segment from t = 2.5 s to t = 7.5 s . The slope is: v₂ = 50 - 50 7.5 - 2.5 = 0 At t = 8 s , the particle is on the line segment from t = 7.5 s to t = 10.0 s . The slope is: v₃ = 100 - 50 10.0 - 7.5 = 50 2.5 = 20 m/s At t = 12 s , the parti