I've made a drawing in order to visualize the problem better: 1. The problem statement, all variables and given/known data A car can increase its speed only at 3.00 m/s2, move at constant velocity, or decrease its speed at 7.00 m/s2. Starting at rest, the driver wishes to drive to a road sign located at x=100 m. He increases his speed, then travels at constant velocity and then decreasing his speed. The driver begins accelerating at t=0 and switches to constant velocity at t=4.50 s. At what position must the driver switch from constant velocity to decreasing speed if he wants to stop the car at the road sign? 2. Relevant equations These are the kinematic equations I used to solve the problem: x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2 v1=v0+a0(t1-t0) v32=v22 + 2a2(x3-x2) 3. The attempt at a solution x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2 x1=1/2a0t12 = x1=1/2(3.0m/s2)(4.50s)2 = 30.4m v1=v0+a0(t1-t0) v1=(3.0m/s2)(4.50s) = 13.5m/s Since after v1 the velocity is constant, v2 must be constant and equal to 13.5m/s v32=v22 + 2a2(x3-x2) -v22=2a2x3-2a2x2 x2=-[-(v22-2a2x3) / 2a2] x2 = -[(-182.25+1400)/-14] = 86.98m Does this result look right?