Question

A car accelerates uniformly from rest to a speed of 45.0 mi/h in 14.0 s.(a) Find the distance the car travels during this time._____ m(b) Find the constant acceleration of the car._____ m/s2

Answer 1

(a) 141. 12 m

(b) 1.44 m/s²

Explanation:

Given:

Time (t) = 14 s

Speed (v) = 45 mi/h

We must convert the speed in meters per second, like this:

`45(mi)/(h)\cdot\frac{1609.34\text{ m}}{1\text{ mi }}\cdot\frac{1\text{ h}}{3600\text{ s}}=20.12\text{ m/s}`

First, we calculate the acceleration as follows:

`\begin{gathered} a=(\Delta v)/(\Delta t) \\ \\ \text{ we replacing:} \\ \\ a=(20.12)/(14)=1.44\text{ m/s}^2 \end{gathered}`

and the distance is determined like this:

`\begin{gathered} d=ut+(1)/(2)at^2 \\ \\ \text{ we replacing} \\ \\ d=0\cdot14+(1)/(2)\cdot1.44\cdot14^2 \\ \\ d=141.12\text{ m} \end{gathered}`