Question

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

• A. 3 m
• B. 9 m
• C. 10 m
• D. 6 m

Hint:

Displacement equals the area under the v-t graph from t = 0 to t = 5 s.

Answer 1

The Correct Option is B

Use kinematics piece by piece. 0-2 s: acceleration \(a=1\ \mathrm{m/s^2}\), so \(x_1=\frac12(1)(2)^2=2\) m. 2-4 s: constant \(v=2\) m/s, \(x_2=2\times2=4\) m. 4-5 s: constant \(v=3\) m/s, \(x_3=3\times1=3\) m.
\(x(5)=2+4+3=9\) m.
Answer: (2) 9 m