A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 m

Question

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance of 135 m in t seconds. The value of t is:

Accepted Answer

1.  **Identify Given Values:**
    *   Initial velocity ($v_0$ or $u$) = 10 ms⁻¹
    *   Final velocity ($v$) = 20 ms⁻¹
    *   Displacement ($x$ or $s$) = 135 m
    *   Time interval = $t$
2.  **Select Kinematic Equation:**
    For uniformly accelerated motion, the displacement is equal to the average velocity multiplied by the time interval:
    $$ x = \left( \frac{v + v_0}{2} ight) t $$ 
3.  **Calculation:**
    Substitute the known values into the equation:
    $$ 135 = \left( \frac{20 + 10}{2} ight) t $$
    $$ 135 = \left( \frac{30}{2} ight) t $$
    $$ 135 = 15t $$
    $$ t = \frac{135}{15} = 9 	ext{ s} $$

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