First slide

Rectilinear Motion

Question

A body starts from rest and travels with a uniform acceleration of $5 m / s^{2}$ and then decelerates at a uniform rate of $3 m / s^{2}$ again to come to rest. Total time of travel is 10s . Then the maximum velocity attained by the body is

Moderate

Solution

Acceleration $a_{1} = 5 m / s^{2}$
Deceleration $a_{2} = 3 m / s^{2}$
Total time $T = 10 S$ .
$∴$ The maximum velocity attained
$\begin{array}{l} V_{max} = (\frac{a_{1} a_{2}}{a_{1} + a_{2}}) T \\ = (\frac{5 \times 3}{8}) \times 10 \\ = \frac{150}{8} \\ = 18.75 m / s \end{array}$

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