Car and bicycle collision problem

[Ishfa]

Homework Statement

Is the answer, xc = v0t -c( t - t1 )^3 /6 or xc(t)=v0t1+v0(t−t1)−c(t−t1)^3 /6 ? Which one is correct and why?

Relevant Equations

a = -c (t - t1)

 

[PeroK]

Homework Statement: Is the answer, xc = v0t -c( t - t1 )^3 /6 or xc(t)=v0t1+v0(t−t1)−c(t−t1)^3 /6 ? Which one is correct and why?

Those two expressions are equal!

 

[kuruman]

The expressions may be equal, but neither of them can be considered the answer. Variable "t" in these expressions is "any time t". How do these answers reflect the fact that the car stops at t = t₂?
Hint: x_c(t) is a piecewise continuous function.

 

[PeroK]

Hint: x_c(t) is a piecewise continuous function.

It's actually a continuous function.

 

[PeroK]

PS it's actually a Spline function - continuous and piecewise polynomial in $t$.

 

[kuruman]

PS it's actually a Spline function - continuous and piecewise polynomial in $t$.

I defer the appellation details to you. I just wanted to convey the "piecewise" and "continuous" ideas to the OP.

 

[nasu]

What's with the bicycle? Is there a part (b)?