Question

1. kaya is riding her dirt bike eastward on a dirt road. she spots a pothole ahead. kaya slows her car from 14.0 m/s to 5.5 m/s in 6.0 s. what is her acceleration? 7) how long would it take jesse with an acceleration of -2.50 m/s² to bring his bicycle with an initial velocity of 13.5 m/s to a complete stop?

Explanation:

Step1: Define acceleration formula

Acceleration is $\frac{\text{final velocity}-\text{initial velocity}}{\text{time}}$, so $a=\frac{v_f - v_i}{t}$

Step2: Plug in Kaya's values

$v_i=14.0\ \text{m/s}$, $v_f=5.5\ \text{m/s}$, $t=6.0\ \text{s}$
$a=\frac{5.5 - 14.0}{6.0}\ \text{m/s}^2$

Step3: Calculate Kaya's acceleration

$a=\frac{-8.5}{6.0}\approx -1.42\ \text{m/s}^2$

Step4: Rearrange formula for time

$t=\frac{v_f - v_i}{a}$

Step5: Plug in Jesse's values

$v_i=13.5\ \text{m/s}$, $v_f=0\ \text{m/s}$, $a=-2.50\ \text{m/s}^2$
$t=\frac{0 - 13.5}{-2.50}\ \text{s}$

Step6: Calculate Jesse's time

$t=\frac{-13.5}{-2.50}=5.4\ \text{s}$

Answer:

1. Kaya's acceleration: $\approx -1.42\ \text{m/s}^2$
2. Time for Jesse to stop: $5.4\ \text{s}$