Question

In a test run, a certain car accelerates uniformly from zero to 22.0 m/s in 2.00 s.(a) What is the magnitude of the car's acceleration? ________ m/s2(b) How long does it take the car to change its speed from 11.0 m/s to 22.0 m/s? _________ s

Answer 1

Answer:

(a) 11 m/s²

(b) 1 s

Explanation:

First, we need to calculate the magnitude of the car's acceleration using the following

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

Where vf is the final velocity, vi is the initial velocity and t is the time. Replacing vf = 22 m/s, vi = 0 m/s and t = 2.00 second, we get:

$a=\frac{22\text{ m/s - 0 m/s}}{2\text{ s}}=\frac{22\text{ m/s}}{2\text{ s}}=\text{ 11 m/s}^2$

Then, we can calculate the time that it takes to change its speed from 11.0 m/s to 22 m/s by solving the first equation for t, so

$\begin{gathered} at=v_f-v_i \\ \\ t=\frac{v_f-v_i}{a} \end{gathered}$

Replacing vf = 22.0 m/s, vi = 11.0 m/s and a = 11 m/s², we get:

$t=\frac{22\text{ m/s -11m/s}}{11\text{ m/s}^2}=\frac{11\text{ m/s}}{11\text{ m/s}^2}=1\text{ s}$

Therefore, the answers are

(a) 11 m/s²

(b) 1 s