A car is moving at 20 m/s. The driver applies the brakes and the car decelerates at 1 m/s2. How long will it take the car to stop and how far will it travel until it stops
oh that's easy. you have to use ì. 20m/s = Velocity...a= Äv(velocity) over Ät(time) so it would be 20m/s divided by 1m/s and you get 20m/s squared and so on...hope it helps!
20m^2
To find the time it takes for the car to stop, we can use the formula:
\(v = u + at\)
where:
v = final velocity (0 m/s since the car stops)
u = initial velocity (20 m/s)
a = acceleration (-1 m/s^2 since the car is decelerating)
t = time
Rearranging the formula, we have:
\(t = \frac{{v - u}}{{a}}\)
Substituting the values, we get:
\(t = \frac{{0 - 20}}{{-1}} = 20\) seconds
Therefore, the car will take 20 seconds to stop.
To find the distance traveled until the car stops, we can use the formula:
\(s = ut + \frac{1}{2}at^2\)
where:
s = distance
u = initial velocity (20 m/s)
t = time (20 seconds)
a = acceleration (-1 m/s^2)
Substituting the values, we get:
\(s = 20 \times 20 + \frac{1}{2} \times -1 \times 20^2\)
Calculating this equation, we find:
\(s = 400 - 200 = 200\) meters
Therefore, the car will travel 200 meters until it stops.
To find the time it takes for the car to stop, we can use the equation:
\[ \text{time} = \frac{\text{final velocity} - \text{initial velocity}}{\text{deceleration}} \]
Given that the initial velocity (\(v_0\)) is 20 m/s, the final velocity (\(v\)) is 0 m/s when the car stops, and the deceleration (\(a\)) is -1 m/s² (negative because it is a deceleration), we can plug in the values:
\[ \text{time} = \frac{0 - 20}{-1} \]
Simplifying the equation, we get:
\[ \text{time} = \frac{20}{1} = 20 \, \text{s} \]
Therefore, it will take the car 20 seconds to stop completely.
To find the distance the car will travel until it stops, we can use the equation:
\[ \text{distance} = \frac{(\text{initial velocity} + \text{final velocity})}{2} \times \text{time} \]
Plugging in the values we have:
\[ \text{distance} = \frac{(20 + 0)}{2} \times 20 \]
Simplifying further:
\[ \text{distance} = \frac{20}{2} \times 20 = 200 \, \text{m} \]
Therefore, the car will travel a distance of 200 meters until it stops.