Displacement is area under velocity-time graph

Steps:

• Displacement from X is the area under the v-t curve from t=0 to t=0.8 s.
• The graph is a straight line from v=0 at t=0 to v=4 m/s at t=0.8 s, forming a right triangle.
• Calculate area: (1/2) × base (0.8 s) × height (4 m/s) = 1.6 m.

Why A is correct:

• Displacement equals the integral of velocity with respect to time, given by the triangle area formula as 1.6 m.

Why the others are wrong:

• B: 1.8 m assumes a slightly larger area, ignoring the exact triangular shape from rest.
• C: 2 m uses an incorrect average velocity of 2.5 m/s instead of 2 m/s for uniform acceleration.
• D: 3.2 m treats velocity as constant at 4 m/s, which overestimates by ignoring the initial zero velocity.

Final answer: A