Question

A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup?

Short answer

The required constant deceleration is\(4.81{\rm{ m/}}{{\rm{s}}^2}\).

Step-by-step solution

Kinematic formula

Here, we need to use the kinematic formula.

The kinematic formula is,

\(v_f^2 = v_i^2 + 2aD\)-------(1)

Where, \({v_f}\) is final velocity, which is equal 0, \({v_i}\) is the initial velocity, which is \(27.73{\rm{ m/s}}\), \(a\) is acceleration, and \(D\) is the distance travelled, which is 80.

Here we change \(\frac{{km}}{h}\) into \(\frac{m}{s}\).

Find the acceleration

Here, first we will change \({\rm{km/h}}\) into \({\rm{m/s}}\) as follows:

\(\begin{aligned}{c}100{\rm{ km/h}} &= 100 \times \frac{{1000{\rm{ m}}}}{{3600{\rm{ s}}}}\\ &= 27.73{\rm{ m/s}}\end{aligned}\)

Put the all value in equation (1)

\(\begin{aligned}{c}v_f^2 - v_i^2 &= 2a \times 80\\{0^2} - {\left( {27.73} \right)^2} &= 160a\\a &= \frac{{ - {{\left( {27.73} \right)}^2}}}{{160}}\\ &\approx 4.81\end{aligned}\)

Hence, the required constant deceleration is \(4.81{\rm{ m/}}{{\rm{s}}^2}\).