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?

Question

stormfire1 · Answer

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