Question

a car starts from rest and travels for 4.3 seconds with a uniform acceleration of +1.2 m/s^2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s^2. The brakes are applied for 1.5 seconds. how far has the car gone from its start?

Answer 1

Break the problem into 3 parts:

First part - find the distance traveled while under a positive acceleration:
V0 = 0 m/s
X0 = 0 m a = 1.2 m/s^2
t = 4.3 s

Plug in the values into the kinematic formula:
X = X0 + V0t + 1/2 at^2
So you get X = 0m + 0m/s + 1/2 * (1.2m/s^2) * (4.3s)^2 = 11.094 meters

Second part: Final the velocity it is at when you begin to brake:
V = V0 + at = 0m/s + (1.2m/s^2) * 4.3s = 5.16 m/s

Finally, find out how far you've traveled overall using the formula:
X = X0 + V + 1/2 at^2
So you get X = 11.094m + (5.16m/s) + 1/2 (-1.2m/s^2)*(1.5s)^2 = 14.904m