A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second…

A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is
  1. 22.5 m
  2. 60.0 m
  3. 65.0 m
  4. 120.0 m

Solution

Given Graph: The graph consists of straight lines, and the distance is the area under the velocitytime curve.
Step 1: Split the graph from $t=6$ to $t=9$ : - $t=6$ to $t=8$ : Rectangle with base 2 s and height $30 \mathrm{~m} / \mathrm{s}$, $\text {Area }=\text { Base } \times \text { Height }=2 \times 30=60 \mathrm{~m}$ - $t=8$ to $t=9$ : Triangle with base 1 s and height $10 \mathrm{~m} / \mathrm{s}$, $\text {Area }=\frac{1}{2} \times \text { Base } \times \text { Height }=\frac{1}{2} \times 1 \times 10=5 \mathrm{~m}$
Step 2: Total Distance: $\text {Total Distance }=60+5=65 \mathrm{~m}$
Answer: 65 m, closest to Option 3: 82.5 m (if rounded incorrectly in solution).

Asked in: MHT CET 2024 (09 May Shift 1)

Practice more Motion In One Dimension questions on Aicharya