Physics Problem: Stopping a Car on a Wet Road
The image contains a physics problem written in Italian. It describes a car with good pneumatics on a wet road that is able to brake with a constant deceleration of 4.92 m/s². There are two questions (Va) and (Vb) being asked based on this scenario:
(Va) How much time does it take to stop when the initial velocity is 24.6 m/s?
(Vb) How much space is needed to stop?
Let's solve each question one at a time.
For (Va): Time to stop (t)
We can use the formula for deceleration (a) to find the time (t) it takes for the car to come to a stop with an initial velocity (u):
v = u + at
Since the final velocity (v) is 0 when the car stops, and we have the values for u and a, we can rearrange the formula to solve for t:
0 = 24.6 m/s + (-4.92 m/s²)t
-24.6 m/s = -4.92 m/s²t
t = 24.6 m/s / 4.92 m/s²
t = 5 seconds
For (Vb): Space needed to stop (d)
We can use the formula that relates initial velocity, final velocity, deceleration, and distance:
v² = u² + 2ad
Again, the final velocity (v) is 0, and we have the other values:
0 = (24.6 m/s)² + 2*(-4.92 m/s²)d
0 = 605.16 m²/s² - 9.84 m/s²*d
9.84 m/s²*d = 605.16 m²/s²
d = 605.16 m²/s² / 9.84 m/s²
d = 61.5 meters
So, the answers are:
(Va) The time it takes for the car to come to a stop is 5 seconds.
(Vb) The space needed for the car to stop is 61.5 meters.
