You drive on Interstate 10 from San Antonio to Houston, half the time at 54 km/h

(a)The interstate 10 travels at v₁ = 54 km/h for atime t₁ = (t/2),where t is the total time of travel fromsan Antonio toHouston.The other half at v₂ = 90 km/hfor a time t₂ = (t/2).The average speed from San Antonio to Houston isV = [(v₁t₁ +v₂t₂)/(t₁ + t₂)]or V = [(t/2) * (54 + 90)/(t)] = 72 km/h(b)The average speed from Houston back to San Antonio isV = (Total distance/Total time) = [(d)/((d/2)/90) +((d/2)/54)]or V = 16.875 km/h(c)The average speed for the entire trip isV = [(72 + 16.875)/(2)] = 44.43 km/h(d)The average velocity for the entire trip isV = [(72 - 16.875)/(2)] = 27.56 km/h(e)The graph of x versus t for (a) is linear.This is becausethe position of the vehicle changes in equal intervals of time.Thatis the vehicle travelshalf the time at one speed and the remaininghalf at other speed.(f)The average velocity can be found on a graph of x versus tby considering the points for position for which the vehicletravels half the time at onespeed and the other half at adifferent speed.