A car will skid to a halt at a uniform rate of -9.4 m/s^2. If you measure skid marks that are 34 m long, with what speed was the car going just before the driver slammed the brakes?
time = √(2 * distance / acceleration)
initial velocity = 2 (distance / time)
To find the initial speed of the car before braking, we need to use the following kinematic equation of motion:
v^2 = u^2 + 2as,
where:
v = final velocity (0 m/s, as the car comes to a halt)
u = initial velocity (what we need to find)
a = acceleration (-9.4 m/s^2, negative since it is deceleration)
s = distance traveled (34 m)
Rearranging the equation, we have:
u^2 = v^2 - 2as.
Substituting the values:
u^2 = 0^2 - 2(-9.4)(34).
u^2 = 632.8.
Taking the square root of both sides to solve for u:
u = √632.8.
u ≈ 25.16 m/s (rounded to two decimal places).
Therefore, the car was traveling at approximately 25.16 m/s (or 25.2 m/s to one decimal place) just before the driver slammed the brakes.
To find the speed of the car just before the driver slammed the brakes, we can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s because the car comes to a halt)
u = initial velocity (speed of the car before slamming the brakes)
a = acceleration (-9.4 m/s^2)
s = distance (34 m)
Since the car comes to a halt, the final velocity (v) is 0 m/s. We can plug in the values into the equation and solve for u:
0^2 = u^2 + 2(-9.4)(34)
Simplifying:
0 = u^2 - 638.8
Rearranging the equation:
u^2 = 638.8
Taking the square root of both sides:
u = √638.8
Calculating the square root:
u ≈ 25.28 m/s
Therefore, the speed of the car just before the driver slammed the brakes was approximately 25.28 m/s.