Question

A certain roller coaster can accelerate at 20 ft/s/s. How far will the roller coaster travel if it accelerates from rest for 5 s?

**please show work and explain

Answer 1

Answer:

• A roller coaster can accelerate at 20 ft/s²
• Initial velocity = 0 m/s
• Time = 5 s
• Distance = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• Here we may use the second equation of motion as we are given the initial velocity, the time, and the acceleration then the only Equation that connects them is this only Equation. Before that we shall convert the acceleration from ft/s² to m/s²
• Here we took the initial velocity as 0 m/s because of its given that the body starts from rest

$\displaystyle\sf :\implies 20 \div 3.281$

$\displaystyle\sf :\implies \dfrac{20}{3.281}$

$\displaystyle\sf :\implies \red{Acceleration = 6.096}$

$\displaystyle\underline{\bigstar\:\textsf{Distance covered :}}$

$\displaystyle\sf \dashrightarrow s = ut+\dfrac{1}{2}at^2$

$\displaystyle\sf \dashrightarrow s = 0\times 5+\dfrac{1}{2}\times 6.096\times 5^2$

$\displaystyle\sf \dashrightarrow s = 0+\dfrac{1}{2} \times 6.096\times 25$

$\displaystyle\sf \dashrightarrow s = 3.048\times 25$

$\displaystyle\sf \dashrightarrow \underline{\boxed{\sf Distance = 76.2 \ m}}$

$\displaystyle\therefore\:\underline{\textsf{The roller coaster will cover a distance of \textbf{ 76.2 m }}}$

In the Formula

⨳ s = Distance

⨳ u = Initial Velocity

⨳ t = Time

⨳ a = Acceleration