Question

Traveling in the city its faster to take a bicycle than a bus, one reason for this is that a bike can accelerate faster than a bus. Let’s say a Bike and bus both stopped at a red light and both takes off an exact same time when the light turns green. The bike accelerates at 1.2 m/s2 with a vmax of 12 m/s . The bus on the other hand has an acceleration of 0.8 m/s2 with a vmax of 20 m.s. The bike has a higher initial acceleration so it will be in front of the bus for some time. How much time elapses until the bus catches up with the biker.
Abus: 0.8 m/s2
Vmax: 20 m/s
Abike: 1.2 m/s2
Vmax: 12 m/s

Answer 1

a₁=0.8 m/s²
v₁=20 m/s
a₂=1.2 m/s²
v₂=12 m/s
bike: the time to rich v₂ is
t₂ =v₂/a₂ = 12/1.2 = 10 s.
the distance to the meeting point
-for bike
s= a₂t₂²/2 +v₂(t-t₂)
-for bus
s=a₁t²/2
a₂t₂²/2 +v₂(t-t₂)=a₁t²/2
a₁t² -2 v₂t+2 v₂t₂-a₂t₂²=0
0.8 t²-24t+240-120=0
t²-30t+150=0
t=23.7 s

Answer 2

Thank you so much, you hit it right on the nail