A car with a mass of 1136 kg is coasting in neutral on astraight,level road. It

Question

A car with a mass of 1136 kg is coasting in neutral on astraight,level road. It slows down, and its speed as a function oftime is given by the equation:
v(t) = a- bt +ct2
Constant Value Units a 26.8 m/s b 0.310 m/s2 c 2.10·10-3 m/s2 At a time of 32.0 s the speed, as given by the above equation, is19.03 m/s. Calculate the power which the engine must deliver (tocompensate for air resistance and rolling resistance) in order tomaintain that speed.
Constant Value Units a 26.8 m/s b 0.310 m/s2 c 2.10·10-3 m/s2 v(t) = a- bt +ct2

Explanation / Answer

  Power   P   =   F *v   =   m * a * v    acceleration   a   =   dv/dt   =   d/dt( a - b * t + c *t2)   =   2 * c *t   -   b    =>   P   =   m* (2 * c * t   -   b ) * v    Givenat   t   =   32.0s,   v   =   19.03   m/s    P   =   1136 *( 2 * 2.10 * 10-3 *32.02   -   0.310 ) *19.03   =  8.62 *104    W   =   86.2   kW

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