Question:

The velocity-time graph below represents the motion of an object.

a) Describe the motion of the object during the first 5 seconds.

b) Calculate the acceleration of the object during the time interval t = 5 s to t = 10 s.

c) Determine the total displacement of the object during the time interval t = 0 s to t = 10 s.

Answer:

a) From the graph, we can observe that the object is moving in the positive direction during the first 5 seconds. The velocity decreases uniformly from an initial velocity of 15 m/s to a final velocity of 5 m/s.

b) Acceleration is the rate of change of velocity. To calculate the acceleration during the time interval t = 5 s to t = 10 s, we need to determine the change in velocity and divide it by the time interval.

The change in velocity during this interval can be found by subtracting the initial velocity from the final velocity:

Change in velocity = Final velocity - Initial velocity = 5 m/s - (-5 m/s) = 10 m/s

The time interval is 10 s - 5 s = 5 s.

Acceleration = Change in velocity / Time interval = 10 m/s / 5 s = 2 m/s²

Therefore, the acceleration of the object during the time interval t = 5 s to t = 10 s is 2 m/s².

c) Displacement is a measure of the change in position of an object. To determine the total displacement during the time interval t = 0 s to t = 10 s, we need to find the area under the velocity-time graph.

The area under the velocity-time graph represents the displacement.

The graph can be divided into rectangles and triangles:

Rectangle 1 has a base width of 5 s and a height of 15 m/s: Area of Rectangle 1 = base × height = 5 s × 15 m/s = 75 m

Rectangle 2 has a base width of 5 s and a height of 5 m/s: Area of Rectangle 2 = base × height = 5 s × 5 m/s = 25 m

Triangle 1 has a base width of 5 s and a height of 10 m/s: Area of Triangle 1 = (1/2) × base × height = (1/2) × 5 s × 10 m/s = 25 m

Adding up the areas:

Total Displacement = Area of Rectangle 1 + Area of Rectangle 2 + Area of Triangle 1 = 75 m + 25 m + 25 m = 125 m

Therefore, the total displacement of the object during the time interval t = 0 s to t = 10 s is 125 m.