The car starts off and drives with constant acceleration for 10 seconds. Then it decelerates with an acceleration of 2 times

The car starts off and drives with constant acceleration for 10 seconds. Then it decelerates with an acceleration of 2 times greater until it comes to a complete stop. Find acceleration during acceleration if the entire path is 75 m.

Let’s designate acceleration during acceleration by a, then the acceleration of deceleration will be = 2 a;

Let it consist of two sections a S = S1 + S2;

t = 10; VO = 0;

S1 = a t ^ 2/2 = a 10 ^ 2/2 = 50 a;

during this time the speed will increase from zero, will become V = a t = 10 a;

and this is the initial speed for the second section, we apply the formula without time, remember that in

at the end, the body stops and the speed is zero:

S2 = V ^ 2/2 a ^ 2 = (10 a) ^ 2/2 (2 a) = 100 a ^ 2/4 a = 25 a;

substitute:

S = 75

75 = 50 a + 25 a = 75 a;

a1 = 1 m / s2;

a1 = 2 m / s2;