An electric vehicle starts from rest and accelerates at a rate of 1.8 m/s2 in a straight line until it reaches a speed of 17 m/s. the vehicle then slows at a constant rate of 1.0 m/s2 until it stops. how far does the vehicle move from start to stop?

I think the easy way to do this is to break it into two parts. There might be a simpler way, but you want to understand both steps.

Acceleration

a = 1.8 m/s^2
vi = 0 m/s
vf = 17 m/s
d =

formula

vf^2 = vi^2 + 2ad

Substitute and solve
17^2 = 0^2 + 2*1.8*d
289 = 3.6 d
d = 289 / 3.6
d = 80.3 m

Deceleration

vi = 17 m/s
vf = 0
a = - 1.0 m/s The vehicle is decelerating. The "acceleration" is negative.
d = ???

Note it's the same formula
0^2 = 17^2 + 2*-1*d
- 289 = - 2d
x = 144.5

Total distance = 80.3 + 144.5 = 224.8 meters.

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.

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