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

(a) 11 m/s²

(b) 1 s

Step-by-step explanation:

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

`a=(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=(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