Physics related antiderivatives problemI was wondering if I could get a little help with a calculus related word problem:A car braked with a constant deceleration of 5 meters per second squared for 60 meters before stopping. How fast was the car traveling when the brakes were applied? I can't use the definite integral, only the antiderivative.

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Physics related antiderivatives problemI was wondering if I could get a little help with a calculus related word problem:A car braked with a constant deceleration of 5 meters per second squared for 60 meters before stopping. How fast was the car traveling when the brakes were applied? I can&#039;t use the definite integral, only the antiderivative.

kpgt1z · Accepted Answer

Step 1Let   t  r  a  v  e      l    m    =  a      s    2    +  b  s  +  c (  s  = time, travel_m = travelled distance)                    d        2            y              d              s        2              a      s    2    +  b  s  +  c (The second derivative of distance gives you the acceleration.)  =  2  a  =  −  5  a  =  −  2.5  t  r  a  v  e      l    m    =  −  2.5      s    2    +  b  s  +  cAt first, the travel distance was 0,   c  =  0.  t  r  a  v  e      l    m    =  −  2.5      s    2    +  b  s            d      y              d      s        −  2.5      s    2    +  b  s (The first derivative of distance gives you the speed.)  =  −  5  s  +  b, but at   s  =  0, when the car braked, the speed was b, and they are asking for b.Step 2When it stopped the speed was zero. To see when it stopped:  −  5  s  +  b  =  0  −  2.5      s    2    +  b  s  =  60Substitute:   −      5    2    ×            b      2        25    +            b      2        5    =  60 -&amp;gt;       b    2    =  600.                              b          =          10                      6

watch5826c · Accepted Answer

Step 1You just need the formula      V    1    2    −      V    2    2    =  2  γ  (      X    1    −      X    2    ) with       V    i    = speed at position       X    i   and   γ the constant acceleration.thus       V    1    2    −  0  =  2.5.60      V    1    =      600    m      /    sStep 2The formula comes from the integration of             d      (              V        2                    /            2      )              d      t        =  V            d      V              d      t        =  γ  V  =  γ            d      X              d      t

Physics related antiderivatives problem I was wondering if I could get a little help with a calculu

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