Question

How long will be required for a car to go from a speed of 28.0 m/s to a speed of 31.0 m/s if the acceleration is 3.0 m/s

2
?

Answer 1

It will take 1 second for the car to go from a speed of 28.0 m/s to a speed of 31.0 m/s, given a constant acceleration of 3.0 m/s².

To determine the time required for a car to change speed, we can use the acceleration formula:

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_f=V_o+a* t} \end{gathered}$} }`

Where:

• Vf is the final speed
• Vo is the initial velocity
• a is the acceleration
• t is time

In this case:

• Initial velocity (Vo) = 28.0 m/s
• Final velocity (Vf) = 31.0 m/s
• acceleration (a) = 3.0 m/s²

We clear the formula to calculate the time, then:

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=(\Delta v)/(a) \ \ \rightarrow \ \ t=(V_f-V_o)/(t) } \end{gathered}$} }`

Where:

• t is the time
• Vf is the final velocity
• Vo is the initial velocity
• a is the acceleration

Substituting the values into the formula, we can solve for time (t):

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=(31.0 \ (m)/(s)-28(m)/(s) )/(3.0 \ (m)/(s^2) ) } \end{gathered}$} }`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=\frac{3.0 \ \frac{\\ot{m}}{s} }{3.0 \ \frac{\\ot{m}}{\\ot{s^2}} } } \end{gathered}$} }`

`\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=1.0 \ Second } \end{gathered}$} }}`

It will take 1.0 second for the car to go from a speed of 28.0 m/s to a speed of 31.0 m/s, given a constant acceleration of 3.0 m/s².

Answer 2

We can use the following kinematic equation to solve for the time it takes for the car to accelerate:

`\implies\:\boxed{\:v_f = v_i + at\:}`

where:

• 
  `v_f` is the final velocity (31.0 m/s)
• 
  `v_i` is the initial velocity (28.0 m/s)
• 
  `a` is the acceleration (3.0 m/s²)
• 
  `t` is the time it takes to accelerate

Substituting the given values:

`{\implies 31.0\text{ m/s} = 28.0\text{ m/s} + (3.0\text{ m/s}^2)t}`

Solving for
`t`:

`\begin{aligned}\implies t& = \frac{31.0\text{ m/s} - 28.0\text{ m/s}}{3.0\text{ m/s}^2}\\&=\frac{3.0\text{ m/s}}{3.0\text{ m/s}^(2)}\\&= \bold{1.0\: s}\end{aligned}`

`\therefore` It will take 1.00 second for the car to accelerate from a speed of 28.0 m/s to a speed of 31.0 m/s.

`\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}`