A car is initially travelling at 30m/s, which is above the speed limit. The driver sees a speed limit trap ahead and applies the brakes for 5 seconds, causing the car to slow down by 2m/s every second while the brakes are on.
How far does the car travel while the brakes are being applied?
dv/dt = a = -2 m/s^2
v = 30 - a t
d = Vi t + .5 a t^2
so
d = 30 t - 1 t^2
but t = 5
so
d = 30*5 - 25
= 150 - 25 = 125
To find out how far the car travels while the brakes are being applied, we need to calculate the total distance covered during the 5-second period.
First, we find the initial velocity of the car (v0) when the brakes are applied. The car is initially traveling at 30 m/s, so v0 = 30 m/s.
Next, we find the final velocity of the car (v) after 5 seconds. The car slows down by 2 m/s every second, so after 5 seconds, the final velocity will be v = v0 - (2 m/s * 5 s).
v = 30 m/s - (2 m/s * 5 s) = 30 m/s - 10 m/s = 20 m/s.
Now, we can use the equation of uniform acceleration to calculate the distance covered (d) during the 5-second period:
d = (v0 + v) / 2 * t,
where t is the time in seconds.
Substituting the values:
d = (30 m/s + 20 m/s) / 2 * 5 s = 50 m/s / 2 * 5 s = 25 m/s * 5 s = 125 m.
Therefore, the car travels a distance of 125 meters while the brakes are being applied.