Question

What constant acceleration is required to increase the speed of a car from 30 mi/h to 50 mi/h in 5 s?

Short answer

Constant acceleration is \(1.78816{\rm{ m/}}{{\rm{s}}^{\rm{2}}}\).

Step-by-step solution

Formula for Acceleration

The formula for acceleration is given as,

\(a = \frac{{\left( {{\rm{Final velocity}} - {\rm{Initial velocity}}} \right)}}{{{\rm{Change in time}}}}\)

It is given that, \({\rm{Final velocity }} = 50{\rm{ mi/h}}\), \({\rm{Initial velocity }} = {\rm{30 mi/h}}\) and \({\rm{Change in time }} = {\rm{ 5 sec}}\).

Find Acceleration

It is known that, \(1{\rm{ mi/h}} = 0.44704{\rm{ m/s}}\).

Now we change \(\frac{{{\rm{mi}}}}{{\rm{h}}}\) to \(\frac{{\rm{m}}}{{\rm{s}}}\).

\(\begin{aligned}{c}30{\rm{ mi/h}} &= 30 \times 1{\rm{ m/s}}\\ &= 30 \times 0.44704{\rm{ m/s}}\\ &= 13.4112{\rm{ m/s}}\end{aligned}\)

And \(50{\rm{ m/h}} = 50 \times 1{\rm{ m/s}}\).

\(\begin{aligned}{c}50{\rm{ m/h}} &= 50 \times 0.44704{\rm{ m/s}}\\ &= 22.352{\rm{ m/s}}\end{aligned}\)

Put the value in this formula, \(a = \frac{{\left( {{\rm{Final velocity}} - {\rm{Initial velocity}}} \right)}}{{{\rm{Change in time}}}}\).

We get,

\(\begin{aligned}{c}a &= \frac{{\left( {22.352 - 13.4112} \right)}}{5}\\ &= \frac{{8.9408}}{5}\\ &= 1.78816{\rm{ m/}}{{\rm{s}}^2}\end{aligned}\)

Hence, the required acceleration is \(1.78816{\rm{ m/}}{{\rm{s}}^2}\).