Question

Figure shows the velocity-time graph of a particle moving in a straight line. Find the displacement of particle at t$=6$s.

Answer 1

We know, area under the velocity-time graph represents displacement of particle.
D𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑖𝑛 6 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑓𝑜𝑟𝑚𝑒𝑑 𝑏𝑦 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒 𝑔𝑟𝑎𝑝ℎ 𝑎𝑛𝑑 𝑡𝑖𝑚𝑒 𝑎𝑥𝑖𝑠
$=\frac{1}{2}\times 6s\times 2m{s}^{-1}$
$=6$ 𝑚
Hence, the displacement of a particle at t $=6$ s is $6$ m.