A car is travelling at 60km/h when applies his brakes.If the car decelerates uniformly at 5.6m/s2,how far does the car go after the brakes are applied before coming to rest?
well, 60 km/hr = 16.67 m/s
v(t) = 16.67 - 5.6t
set v=0 and solve for t, then plug that into
s(t) = 16.67t - 2.8t^2
200
To find the distance the car travels after the brakes are applied before coming to rest, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s because the car comes to rest)
u = initial velocity (60 km/h or 16.67 m/s)
a = acceleration (deceleration in this case, -5.6 m/s^2)
s = distance traveled
First, let's convert the initial velocity from km/h to m/s:
u = 60 km/h = 60 * (1000/3600) = 16.67 m/s
Now let's substitute the values into the equation:
0^2 = 16.67^2 + 2 * (-5.6) * s
Simplifying the equation:
0 = 277.5644 - 11.2s
Rearranging the equation to solve for s:
11.2s = 277.5644
s = 277.5644 / 11.2
s ≈ 24.80 meters
Therefore, the car travels approximately 24.80 meters after the brakes are applied before coming to rest.