1 A particle is travelling in a straight line. Its velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t\) seconds is given by
$$v = 6 + 4 t \quad \text { for } 0 \leqslant t \leqslant 5$$
- Write down the initial velocity of the particle and find the acceleration for \(0 \leqslant t \leqslant 5\).
- Write down the velocity of the particle when \(t = 5\). Find the distance travelled in the first 5 seconds.
For \(5 \leqslant t \leqslant 15\), the acceleration of the particle is \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Find the total distance travelled by the particle during the 15 seconds.