Solving Homework: Speed, Acceleration, and Distance

[songoku]

Homework Statement

A car passes point A with speed 10 m/s. After that, the car moves with constant acceleration a m/s² for T seconds before reaching B where the speed at that time is V m/s. Then it moves with constant speed for 10 s and reaches C. From C, it moves with acceleration 3 m/s² for T seconds and reaches D with speed 20 m/s.
a. Find V
b. Given that the distance A - D = 675 m, find a and T

Homework Equations

dynamic

The Attempt at a Solution

From A to B
V = 10 + aT...(1)
s₁ = 10T + 0.5 x a x T²

From B to C
s₂ = 10 V

From C - D
20 = V + 3T...(2)
s₃ = V.T + 0.5 x 3 x T²

s₁+s₂+s₃ = 675 ---- >After a few working and using equation 1 and 2, I got:
3T² - 5T + 475 = 0

From last equation, the value of T is imaginary. Where is my mistake or I even interpret the question wrongly?

Thanks

 

[gneill]

Is it possible that the distance A - D lacks a "direction" specification, so that it may in fact be -675m ?

 

[songoku]

I don't know. But with current question like this, is it unsolvable?

 

[gneill]

The question uses "speed" to describe the motions. Speed can be positive or negative. Similarly, the distance specification makes no reference to direction (in fact there is no coordinate system specified anywhere in the problem statement). So I think that it's possible that there there may be one or more solutions depending upon what assumptions you're willing to make.

(I do realize that this is probably not very helpful!)

 

[songoku]

I get your point. Looks like I really have to make assumption to solve this one. Thanks