A particle starts from rest, accelerates at $2 ext{ m/s}^2$ for $10 ext{ s}$ and then goes for constant sp

Question

A particle starts from rest, accelerates at $2 	ext{ m/s}^2$ for $10 	ext{ s}$ and then goes for constant speed for $30 	ext{ s}$ and then decelerates at $4 	ext{ m/s}^2$ till it stops. What is the distance travelled by it?

Accepted Answer

The motion is divided into three parts:

1.  **Acceleration Phase:**
    *   Initial velocity $u = 0$, Acceleration $a_1 = 2 	ext{ m/s}^2$, Time $t_1 = 10 	ext{ s}$.
    *   Distance $S_1 = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}(2)(10)^2 = 100 	ext{ m}$ .
    *   Final velocity reached $v = u + at = 0 + 2(10) = 20 	ext{ m/s}$.

2.  **Constant Speed Phase:**
    *   Velocity $v = 20 	ext{ m/s}$, Time $t_2 = 30 	ext{ s}$.
    *   Distance $S_2 = 	ext{velocity} 	imes 	ext{time} = 20 	imes 30 = 600 	ext{ m}$.

3.  **Deceleration Phase:**
    *   Initial velocity $u' = 20 	ext{ m/s}$, Final velocity $v' = 0$, Acceleration $a_2 = -4 	ext{ m/s}^2$.
    *   Using $v^2 - u^2 = 2aS$: $0^2 - (20)^2 = 2(-4)S_3$.
    *   $-400 = -8S_3 \implies S_3 = 50 	ext{ m}$ .

**Total Distance:** $S_{total} = S_1 + S_2 + S_3 = 100 + 600 + 50 = 750 	ext{ m}$.

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