Question

Two cars are traveling along a straight line in the same direction, the lead car at 24.7m/s and the other car at 29.9m/s. at the moment the cars are 38.1m apart, the lead driver applies the brakes, causing her car to have an acceleration of -1.96m/s2. how long does it take for the lead car to stop? (in s)

Answer 1

Answer: 12.6 s

We would use the equation of motion:

$v-u=at$

where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.

It is given that the lead car has an initial velocity, $u=24.7\hspace{1mm} m/s$. It decelerates with $a=-1.96 \hspace{1mm} m/s^{2}$ to stop (v=0). we need to calculate the time taken by the lead car to stop.

$\Rightarrow t=\frac{v-u}{a}\\ \Rightarrow t=\frac{0-24.7}{-1.96}=12.6\hspace{1mm} s$