If a car at rest accelerates uniformly to a speed of $144 ext{ km/h}$ in $20 ext{ s}$, then it covers a di

Question

If a car at rest accelerates uniformly to a speed of $144 	ext{ km/h}$ in $20 	ext{ s}$, then it covers a distance of:

Accepted Answer

1.  **Convert Units:** First, convert the final speed from km/h to m/s.
    $v = 144 	ext{ km/h} = 144 	imes \frac{5}{18} 	ext{ m/s} = 40 	ext{ m/s}$.
2.  **Identify Given Values:**
    *   Initial velocity, $u = 0$ (at rest).
    *   Final velocity, $v = 40 	ext{ m/s}$.
    *   Time, $t = 20 	ext{ s}$.
3.  **Select Formula:** For uniform acceleration, the distance $s$ can be calculated using the average velocity formula: $s = \left(\frac{u + v}{2}ight)t$ . Alternatively, use $v = u + at$ to find acceleration and then $s = ut + \frac{1}{2}at^2$.
4.  **Calculation (Method 1):**
    $s = \left(\frac{0 + 40}{2}ight) 	imes 20$
    $s = 20 	imes 20 = 400 	ext{ m}$.
5.  **Calculation (Method 2):**
    $a = \frac{v - u}{t} = \frac{40 - 0}{20} = 2 	ext{ m/s}^2$.
    $s = 0(20) + \frac{1}{2}(2)(20)^2 = 400 	ext{ m}$.

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