Answer to Question #341829 in Physics for Dennis

Question

A car starts from rest as accelerated uniformly at a rate of 2m/s^2 for 6s .it then maintains the constant speed for 30s,the breaks are then apllied and vehicle uniformly retands to rest in 5s .find the maximum speed reached at the total distance covered.

Answer 1

The maximum speed reached by a car

$$v=at_1\\ =\rm 2\: m/s^2*6\: s=12\: m/s$$

The total distance covered by a car

$$d=d_1+d_2+d_3=at_1^2/2+vt_2+v/2t_3\\ ={\rm 2\: m/s^2*(6\: s)^2/2+12\: m/s*30\: s}\\ \rm+(12\: m/s)/2*5\: s=426\: m$$