I'm a hurry to go to work today because I forgot to set my alarm clock and woke up late. I'm driving my car very fast, with a velocity of v=40 m/s and coming up to an intersection with a stoplight. When the distance between my car and the intersection is L=100 m, the light turns yellow and I immediately hit the brakes and start to slow down with a constant acceleration. Find the magnitude of my acceleration in m/s2 if my car stops right at the intersection.
V^2 = Vo^2 + 2a*d.
a = (V^2-Vo^2)/2d
a = (0-(40)^2)/200 = -8 m/s^2.
To determine the magnitude of your acceleration, we can use the kinematic equation that relates acceleration, initial velocity, final velocity, and distance.
The equation we'll use is:
(v^2 - u^2) = 2as
Where:
v = final velocity (0 m/s since your car stops)
u = initial velocity (40 m/s)
a = acceleration (which you want to find)
s = distance (100 m)
Rearranging the equation to solve for acceleration (a), we have:
a = (v^2 - u^2) / 2s
Substituting the given values into the equation, we get:
a = (0^2 - 40^2) / (2 * 100)
Simplifying, we have:
a = (-1600) / 200
a = -8 m/s^2
Therefore, the magnitude of your acceleration is 8 m/s^2.
Note: The negative sign indicates that the acceleration is in the opposite direction of your initial velocity (deceleration).