(Solved): Show your work! 3. Starting from rest, a particle first accelerates at acceleration \( a \) throu ...

Show your work!

3. Starting from rest, a particle first accelerates at acceleration \( a \) through a distance \( d \), then it continues at constant speed for time \( t \), and finally decelerates at \( a / 4 \) before coming to rest. If the total distance traversed is \( 20 d \), then \( d \) can be written as \( d=\phi t^{2} \), what is \( \phi \) ? \( (5 \mathrm{pts}) \)