First slide

Rectilinear Motion

Question

Two particles P and Q start from rest and move for equal time on a straight line. Particle P has an acceleration of X m/s² for the first half of the total time and 2X m/s² for
the second half. The particle Q has an acceleration of 2X m/s² for the first half of the total time and Xm/s² for the second half. Which particle has covered larger distance?

Difficult

A

both have covered the same distance
B

P has covered the larger distance
C

Q has covered the larger distance
D

none of these

Solution

$\begin{array}{l} For P, in t \sec . \\ \begin{array}{l} x_{1} = \frac{1}{2} X t^{2} = \frac{X t^{2}}{2} \Rightarrow v_{1} = X t \\ x_{2} = (X t) t + \frac{1}{2} 2 X t^{2} \Rightarrow x_{2} = 2 X t^{2} \\ x_{p} = x_{1} + x_{2} = \frac{5}{2} X + 2 \end{array} \end{array}$
$\begin{array}{l} For Q, \\ \begin{array}{l} y_{1} = \frac{1}{2} (2 X) t^{2} = X t^{2} \Rightarrow v_{2} = 2 X t \\ y_{2} = (2 X t) t + \frac{1}{2} X t^{2} = \frac{5}{2} X t^{2} \\ y_{Q} = y_{1} + y_{2} = \frac{7}{2} X t^{2} \Rightarrow y_{Q} > x_{P} \end{array} \end{array}$

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