Question

a car slams on its brakes, coming to a complete stop in 4.0 s. the car was traveling north at 60.0 mph. calculate the acceleration.

Explanation:

Step1: Recall the acceleration formula

Acceleration \( a \) is defined as the change in velocity \( \Delta v \) over the change in time \( \Delta t \), so \( a=\frac{\Delta v}{\Delta t} \).

Step2: Determine initial and final velocities

The initial velocity \( v_i = 60.0\) mph (north), and the final velocity \( v_f = 0\) mph (since it stops). So \( \Delta v=v_f - v_i=0 - 60.0=- 60.0\) mph.

Step3: Determine the time interval

The time \( \Delta t = 4.0\) s.

Step4: Calculate acceleration

Substitute into the formula: \( a=\frac{-60.0\ \text{mph}}{4.0\ \text{s}}=- 15\ \text{mi/h/s}\).

Step5: Determine the direction

Since the car was moving north and is decelerating (acceleration is opposite to velocity), the direction of acceleration is south (S), because it opposes the northward motion.

Answer:

-15 mi/h/s, S