Physics/Calculus Help: Stopping Distance Calculation for a Decelerating Vehicle

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1. A motorist who was traveling at a speed of 90 feet per second, sees a traffic pile-up ahead and begins to decelerate at a constant rate of 30 feet per second. How war will the vehicle travel before it comes to a complete stop?



2. v=ds/dt
a=dv/dt



3.da/dt=-30
dv/dt=-30t+C
C=90
dv/dt=-30t+90
t=3 when velocity is 0 however I am stuck at how to get the distance traveled
 
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calculusguru said:
1. A motorist who was traveling at a speed of 90 feet per second, sees a traffic pile-up ahead and begins to decelerate at a constant rate of 30 feet per second. How war will the vehicle travel before it comes to a complete stop?



2. v=ds/dt
a=dv/dt



3.da/dt=-30
you mean a = dv/dt = -30 (given)
dv/dt=-30t+C
C=90
watch you calculus...dv/dt = -30
dv/dt=-30t+90
when you integrate, you get v = -30t + C, C =90
t=3 when velocity is 0 however I am stuck at how to get the distance traveled
Now you can integrate your first equation, ds = vdt, where v = -30t +90, and solve for s. Note that once you use calculus to derive the kinematic motion equations that relate v, t, and s, and a, for constant acceleration, then you should memorize them, because you'll use them over and over again. In general, specific equations used to solve specific problems should not be memorized, but there are exceptions when using generally applied equations.
 
you can always use Vf^2=Vi^2+2ad
Vf would be 0 because it means that the motorcycle has stopped.
Vi would be the initial velocity.
a would be the acceleration.
Solve for d.