Question

A bike first accelerates from 0.0m/s to 5.0m/s in 4.5s, then continues at this constant speed for another 4.5s. What is the total distance traveled by the bike

Answer 1

# 1

`\bold{a = ((5-0))/(4.5) = 1.11 m/s^2 }`

`\bold{ v = 0 + a \: t = 1.11 * 4.5 = 5 }`

`\bold{ d = 0 + 0 (4.5) + ((1)/(2))(1.11)(4.5)^2 =11.2 }`

# 2

`\bold{ a = 0 }`

`\bold{ v = 5 }`

`\bold{ d = 11.2 + 5 (4.5) + 0}`

`\bold{ = 11.2 + 22.5 = 33.7 meters}`

Answer 2

Initial speed u= 0.0 m/s

Final speed v= 5.0 m/s

Time t1= 4.5s

Time for constant speed t2=4.5s

to calculate the total distance traveled by the bike:

d = d₁ + d₂

1 = ( v+u/2) × 1₁ + v × 1₂

v = final speed

u = initial speed

t₁ = time for first accelerates

t2 = time for constant speed

d = (5+0/2) × 4.5+ 5.0 x 4.5

d = 33.75m

so, the total distance traveled by the bike is 33.75 m.