78. In this solution, we make use of the notation x(t) for the value of xat a particular t.Thus,x(t) = 50t+ 10t2with SI units (meters and seconds) understood. (a) The average velocity during the first 3 s is given by vxxtavgm/s.=−=+−=()() ( )3050310303802Δ(b) The instantaneous velocity at time tis given by v= dx/dt= 50 + 20t, in SI units. At t= 3.0 s, v= 50 + (20)(3.0) = 110 m/s. (c) The instantaneous acceleration at time tis given by a= dv/dt= 20 m/s2. It is constant, so the acceleration at any time is 20 m/s
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