In coming to a stop, a car leaves skid marks 77 long on the highway Assuming a deceleration of 7.20 , estimate the speed of the car just before braking
To estimate the speed of the car just before braking, we can use the formula of kinematic motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (0, since the car comes to a stop)
- u is the initial velocity (the speed of the car just before braking)
- a is the acceleration (deceleration in this case, which is -7.20 m/s^2 as it opposes the motion)
- s is the displacement (length of the skid marks, which is 77 m)
Rearranging the formula, we get:
u^2 = v^2 - 2as
Since v^2 is 0, the formula becomes:
u^2 = -2as
Plugging in the values we have:
u^2 = -2 * (-7.20) * 77
Calculating this:
u^2 = 1101.60
To find the value of u (the initial velocity), we need to take the square root of both sides:
u = √1101.60
u ≈ 33.18 m/s (rounded to two decimal places)
Therefore, the estimated speed of the car just before braking is approximately 33.18 meters per second.