A student tools along in his new Vette weaving in and out of slow traffic, overtaking little kids boarding the school bus, passing school zones without a second glance, cutting off ambulances and fire trucks, running yellow lights, red lights, yield signs, and stop signs invincible and uncaring in her youth. Suddenly she sees a police car 400 meters ahead. She immediately slams on her brakes and decelerates at -3.5 m/s2 and comes to a complete stop right beside the cop car. She waves and offers the officer a drink from her six-pack. OOPS. The officer shoots the student with a Taser gun and drags the student to jail for truancy.
WHAT WAS THE INITIAL VELOCITY OF THE STUDENT'S CAR just prior to applying the brakes?
I don't know what equations to use... I feel like I am given a very little data to begin with, I don't even know where to start.
vf^2=vi^2+2ad
d=400, a is given, vf=0, solve for vi
To solve this problem, we can use the kinematic equation that relates displacement, initial velocity, acceleration, and time:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity (0 m/s, as the car comes to a complete stop)
vi = initial velocity (what we're trying to find)
a = acceleration (-3.5 m/s^2, as the car decelerates)
d = displacement (400 meters, as given in the question)
Plugging in the known values:
0^2 = vi^2 + 2(-3.5)(400)
Simplifying:
0 = vi^2 - 2800
Rearranging the equation:
vi^2 = 2800
Taking the square root of both sides to isolate vi:
vi = √2800
Calculating the square root of 2800:
vi ≈ 52.92 m/s
Therefore, the initial velocity of the student's car just prior to applying the brakes was approximately 52.92 m/s.