Question

A car initially traveling at 34 m/s slams on the brakes and moves forward 136 m before coming to a complete rest. What was the magnitude of the car's negative acceleration?

a) 8 m/s^2
b) 4 m/s^2
c) 2 m/s^2
d) 1 m/s^2

Answer 1

The magnitude of the car's negative acceleration, or deceleration, is 4.25 m/s^2, with the closest answer option being 4 m/s^2 (option b).

Step-by-step explanation:

The question asks to calculate the magnitude of the negative acceleration of a car that is initially traveling at 34 m/s and stops after moving forward 136 m. Negative acceleration refers to deceleration, which indicates that the car is slowing down. To calculate this, we can use the kinematic equation which relates displacement (s), initial velocity (vi), final velocity (vf), and acceleration (a):

vf2 = vi2 + 2as

Here, the final velocity vf is 0 m/s (since the car comes to a complete rest), the initial velocity vi is 34 m/s, and the displacement s is 136 m. We want to find the acceleration a.

Substitute the known values into the equation:

0 = 342 + 2a(136)

Solving for a gives us:

a = -342 / (2×136) = -1156 / 272 = -4.25 m/s2

The magnitude of the acceleration is positive, so we take the absolute value to get:

|– 4.25 m/s2| = 4.25 m/s2

However, since the provided options are discrete and we calculated an intermediate value, the closest option to our calculated value is 4 m/s2, which is option b).