Question

(8) In the following velocity time graph, the
distance travelled by the body in metres is:
​

Answer 1

To find the distance travelled by any body from the velocity time graph we have to find the area under the graph.

So,

Distance travelled by body in this graph = Area of Triangle ABC + Area of Rectangle + Area of Triangle DEF

Distance travelled = ½ × Base × Height + Length × Breadth + ½ × Base × Height

Distance travelled = ½ × AC × BC + BC × CD + ½ × DF × ED.

Distance travelled = ½ × 10 × 8 + 10 × 8 + ½ × 10 × 8

Distance travelled = $\rm{\dfrac{1}{\cancel{2}}\times{\cancel{10}}\times{8} + 80 + \dfrac{1}{\cancel{2}}\times{\cancel{10}}\times{8}}$

Distance travelled = 40 + 80 + 40 = 160m.

Hence, The Distance travelled by body is 160m.

Answer 2

Answer:

To Find: Distance travelled by the particle.

IMPORTANT!

Area under the velocity time graph shows both displacement and distance travelled.

Here,

∴ Distance travelled = ar(OABC) [Trapezium]

∴ s = ½(OC + AB)(8 m/s)

→ s = ½(30s + 10s)(8 m/s)

→ s = 20s × 8 m/s

→ s = 160 m

∴ The particle covered 160 metres approximately.