First slide

The 3 equation for uniform acc

Question

A particle starts moving from rest from the origin with constant acceleration of $1 m / s^{2}$ and continues to move along X-axis. After sometime it starts moving with constant retardation of $2 m / s^{2}$ and finally stops at a point. If the total distance traversed by the particle is 12 m, its maximum velocity is

Easy

A

8 m/s
B

6 m/s
C

4 m/s
D

2 m/s

Solution

(3)
$\begin{array}{l} V_{m}^{2} = 0 + 2 \times 1 \times x_{1} \Rightarrow x_{1} = \frac{V_{m}^{2}}{2} \\ a n d 0 = V_{m}^{2} - 2 \times 2 \times x_{2} \Rightarrow x_{2} = \frac{V_{m}^{2}}{4} \\ N o w, x_{1} + x_{2} = 12 \Rightarrow \frac{V_{m}^{2}}{2} + \frac{V_{m}^{2}}{4} = 12 \Rightarrow V_{m} = 4 m / s . \end{array}$

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