Question

How long would it take a car starting from rest and accelerating at 5.0 m/s2 to cover a distance of 100 m

Answer 1

t=6.325 s

Step-by-step explanation:

Using the four kinematic equations to answer this question. The four kinematic equations are given as follows.

`\boxed{\left\begin{array}{ccc}\text{\underline{The 4 Kinematic Equations:}}\\\\1. \ \vec v_f=\vec v_0+\vec at\\\\2. \ \Delta \vec x=(1)/(2)(\vec v_f-\vec v_0)t\\\\3. \ \Delta \vec x=\vec v_0t+(1)/(2)\vec at^2\\\\ 4. \ \vec v_f^2=\vec v_0^2+2\vec a \Delta \vec x \end{array}\right}`

We will use equation number three.

`\ \Delta \vec x=\vec v_0t+(1)/(2)\vec at^2`

Where...

• "Δx" is the distance covered by the car (100 m)
• "v_0" is the initial velocity (0 m/s since the car starts from rest)
• "a" is the acceleration (5.0 m/s²)
• "t" is the time we want to find

Plug our known values into the equation and solve for t.

`\ \Delta \vec x=\vec v_0t+(1)/(2)\vec at^2\\\\\Longrightarrow 100=(0)t+\frac12(5.0)t^2\\\\\Longrightarrow 100=(2.5)t^2\\\\\Longrightarrow t^2=40\\\\\Longrightarrow \boxed{t=\pm6.325 \ s}`

Time can't be negative. Thus, t=6.325 s.