Physics Question

Question

A bike first accelerates from 0.0 m/s to 6.5 m/s in 4.5 s, then continues at this constant speed for another 6.0 s. What is the total distance traveled by the bike?

Answer 1

Let

v = 6.5 m/s be the speed the bike achieves after acceleration,

t₁ = 4.5 s be the time the bike accelerates,

t₂ = 6.0 s be the time it rides at the speed v,

s₁ be the distance travelled while accelerating,

s₂ be the distance travelled while at constant speed v.

First we calculate the acceleration a.

For that we need to assume that the acceleration is constant.

By definition of acceleration

a = v/t₁

By a standard formula for acceleration

s₁ = at₁²/2

By definition of speed

s₂ = vt₂

So the total distance

s₁ + s₂ = (v/t₁)t₁²/2 + vt₂ = vt₁/2 + vt₂ = v(t₁/2 + t₂)

Substituting actual values

s₁ + s₂ = 6.5 x (4.5/2 + 6) = 53.625 m