Question

The brakes on your automobile are capable of creating a deceleration of 4.7 m/s2. If you are going 141 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 76 km/h speed limit

Answer 1

Answer:

The minimum time taken is 3.84 s.

Explanation:

The expression for the equation of motion is as follows;

v= u+at

Here, v is the final speed, u is the initial speed, a is the acceleration and t is the time.

Convert the initial speed from $km h^{-1}$ to $m s^{-1}$.

$u=(\frac{141 km}{1 h})(\frac{1000 m}{1 km})(\frac{1 h}{3600 s})$

$u= 39.17m s^{-1}$

Convert the final speed from $km h^{-1}$ to $m s^{-1}$.

$v=(\frac{76 km}{1 h})(\frac{1000 m}{1 km})(\frac{1 h}{3600 s})$

$v= 21.11m s^{-1}$

It is given in the problem that The brakes on your automobile are capable of creating a deceleration of $a= -4.7m s^{-2}$. The sign of the acceleration is negative here as there is deceleration.

Calculate the minimum time by using equation of motion.

v= u+at

Put $u= 39.17m s^{-1}$, $v= 21.11m s^{-1}$ and $a= -4.7m s^{-2}$

21.11= 39.17+(-4.7)t

t= 3.84 s

Therefore, the minimum time taken is 3.84 s.