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.

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

Elena · Answer

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

Emily · Answer

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