3. Consider the motion of the object whose velocity-time graph is given in the diagram. What is the net displacement of the object between times
t = 0 and t = 2?
Velocity-time graph
8
(m/s)
8
12 16
16 m
2 m
8 m
56 m

16 m.

Explanation:

From the question given above, we obtained the following data:

Initial velocity (u) = 0 m/s

Final velocity (v) = 8 m/s

Initial time (t1) = 0 sec

Final time (t2) = 2 secs

Net Displacement (ΔD) =?

Velocity is defined as the rate of change of the displacement of an object with time. Mathematically, it is expressed as:

Change in velocity (Δv) = change in displacement (ΔD) / change in time (Δt)

Δv = ΔD / Δt

Next we shall determine the change in velocity and time. This is illustrated below below:

Initial velocity (u) = 0 m/s

Final velocity (v) = 8 m/s

Change in velocity (Δv) =?

Change in velocity (Δv) = v – u

Change in velocity (Δv) = 8 – 0

Change in velocity (Δv) = 8 m/s

Initial time (t1) = 0 sec

Final time (t2) = 2 secs

change in time (Δt) =?

change in time (Δt) = t2 – t1

change in time (Δt) = 2 – 0

change in time (Δt) = 2 secs.

Finally, we shall determine the net displacement of the object as follow:

Change in velocity (Δv) = 8 m/s

change in time (Δt) = 2 secs.

Net Displacement (ΔD) =?

Δv = ΔD / Δt

8 = ΔD/2

Cross multiply

ΔD = 8 × 2

ΔD = 16 m

Therefore, the net displacement of the object is 16 m.