Question

1. a car, initially traveling at 25 meters per second, is uniformly brought to rest as the brakes are applied over a distance of 40. meters. the magnitude of the average acceleration of the car while braking is

a) 0.31 m/s²
b) 0.63 m/s²
c) 7.8 m/s²
d) 16 m/s²

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v^{2}=v_{0}^{2}+2ax$, where $v$ is the final velocity, $v_{0}$ is the initial velocity, $a$ is the acceleration, and $x$ is the displacement.

Step2: Assign the values

Given $v = 0$ m/s (comes to rest), $v_{0}=25$ m/s, and $x = 40$ m. Substitute into the equation: $0=(25)^{2}+2a\times40$.

Step3: Solve for $a$

First, expand the equation: $0 = 625+80a$. Then, isolate $a$: $80a=- 625$, so $a=\frac{-625}{80}=-7.8125$ m/s². The magnitude of the acceleration is $|a| = 7.8$ m/s².

Answer:

C. $7.8$ m/s²