A driver of a car traveling at 16.7 m/s applies
the brakes, causing a uniform deceleration of
2.5 m/s2.
The first question is - How long does it take the car to accelerate
to a final speed of 13.9 m/s? For this i got 1.12 and that's correct.
The second question is - How far has the car moved during the
braking period?
Could anyone write out the formula and steps to show me how to solve this?
I keep getting 20.272 but i have already been told that it's incorrect.
assuming the 1.12 seconds is correct:
x = xo + vo t + (1/2) a t^2
x = 0 + 16.7 (1.12) + (1/2)(-2.5)(1.12^2)
= 18.7 - 1.6 = 17.1
You seem to have missed the negative sign. Your acceleration is negative. You are braking.
To find the distance the car has moved during the braking period, you can use the following formula:
d = (v^2 - u^2) / (2a)
Where:
d = distance traveled
v = final velocity
u = initial velocity
a = acceleration (negative in this case because it is deceleration)
In this problem, the final velocity (v) is 0 m/s because the car comes to a stop. The initial velocity (u) is 13.9 m/s because the car was initially traveling at that speed. The deceleration (a) is -2.5 m/s^2 because it is in the opposite direction to the motion.
Plugging these values into the formula, we have:
d = (0^2 - 13.9^2) / (2 * -2.5)
d = (-192.81) / (-5)
d = 38.562 m
Therefore, the car has moved a distance of 38.562 meters during the braking period.