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=(v-u)/(a)\\ \Rightarrow t=(0-24.7)/(-1.96)=12.6\hspace{1mm} s`