Question

In coming to a stop, a car leaves skid marks 80 m long on the highway. Calculate the deceleration (negative acceleration) of the car based on the length of the skid marks. Provide the relevant equations used for the calculation.

Answer 1

To calculate the deceleration of a car based on the length of skid marks, use the kinematic equation involving final velocity, initial velocity, acceleration, and displacement. Rearrange the equation and plug in the given values to find the deceleration of the car.

Step-by-step explanation:

To calculate the deceleration of a car based on the length of skid marks, we can use the kinematic equation:

v^2 = u^2 + 2as

Where:

v: final velocity (0, since the car comes to a stop)

u: initial velocity (unknown)

a: acceleration (negative because it is deceleration)

s: displacement (length of skid marks, 80 m)

By substituting the given values and solving for acceleration, we can find the answer.

a = (v^2 - u^2) / (2s)

Since the final velocity is 0, the equation simplifies to:

a = -u^2 / (2s)

Plugging in the values, we get:

a = - (u^2 / (2 * 80))

Therefore, the deceleration of the car is -u^2 / 160.