GATE 2017 ME (ME1) – Question 27

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 1 mark · Numerical answer

The figure shows velocity versus time for straight-line motion. Find the distance travelled from t = 0 to t = 5 s, in metres.

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Correct answer: 10 to 10

Explanation

Velocity is nonnegative over the interval, so distance equals area under the curve. From 0–1 s the triangle gives $1(1)/2=0.5$ m; from 1–2 s the rectangle gives 1 m; from 2–3 s the trapezoid gives $(1+4)(1)/2=2.5$ m; from 3–5 s it gives $(4+2)(2)/2=6$ m. The total is $0.5+1+2.5+6=10$ m.

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