Question

A particle moves in a straight line with the velocity as shown in the figure. At t = 0, x = - 16 m. The graph cuts time axis at $t=24\text{s}$

• A. The maximum value of the position coordinate of the particle is 54 m.
• B. The maximum value of the position coordinate of the particle is 36 m
• C. The particle is at the position of 36 m at t = 18 s
• D. The particle is at the position of 36 m at t = 30 s

Answer 1

Answer: (A), (C), (D)

The correct options are
A The maximum value of the position coordinate of the particle is 54 m.
C The particle is at the position of 36 m at t = 18 s
D The particle is at the position of 36 m at t = 30 s

Maximum value of position coordinate = initial coordinate + area under the graph upto t = 24 s (As upto t = 24 s the displacement of the particle will be positive).

$=-16+\left[\right(2\times 10)+\left(\frac{2+6}{2}\right)\times (18-10)+\frac{1\times 6}{2}\times (24-18\left)\right]$
= - 16 + [20 + 32 + 18] = 54 m
At time t = 18 s
Position = - 16 + Area of graph upto t = 18 s
= - 16 + [20 + 32] = 36 m
At time t = 30 s
Position = - 16 + Area of graph upto t = 30 s
$=-16+[70-\frac{1}{2}\times 6\times 6]=36\text{m}$