Yochanan walked from home to the bus stop at an average speed of 5 km/h. he immediately got on his bus and traveled at an average speed of 60 km/h until he got to school. the total distance from his home to school is 35 kilometers and the entire trip took 1.5 hours. how many kilometers did yochanan cover by walking and travelling on the bus?

Firsly, the speed of Yochanan is not constant. So he has done a motion that contains an acceleration c.

for this type of movment, the equation is X = 1/2ct²+Vit

and with this last, we can find the equation of speed by dX/dt = ct + Vi

so v = ct+Vi

Vi the initial speed

n average speed of 60 km/h until he got to school implies 60=ct + 5,

t = 1.5 hour, so c = 60 - 5 / 1.5 = 56.66

and by using the formula during the motion with the bus)

V²f - V²i = 2. c (xf - xi) so V²f = 3600km/h V²i = 25 km/h

we can find xf - xi = V²f - V²i / 2c, and xf - xi = 31.54 km

but the total distance is 35 km,

so 35km - 31.54km = 3.45 km

yochanan coverd 3.45 kmby walking

yochanan coverd 31.54 km km by riding bus