Question

this velocity-time graph depicts the motion of an object. this velocity-time graph depicts the motion of an object. use the graph to determine the displacement (in meters) of the object during the entire 10.0 seconds. enter your answer accurate to the second decimal place.

Explanation:

Step1: Split graph into two shapes

The graph has a triangle (0-6s) and a rectangle (6-10s).

Step2: Calculate triangle area (displacement)

Area of triangle: $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6.0\ \text{s} \times 25.0\ \text{m/s} = 75.00\ \text{m}$

Step3: Calculate rectangle area (displacement)

Area of rectangle: $\text{length} \times \text{width} = (10.0-6.0)\ \text{s} \times 25.0\ \text{m/s} = 4.0 \times 25.0 = 100.00\ \text{m}$

Step4: Sum the two displacements

Total displacement: $75.00\ \text{m} + 100.00\ \text{m}$

Answer:

175.00 meters