Question

acceleration problems
use the guess method to solve these problems. $a = \frac{\delta v}{t}$
g - write down all \given\ information
u - write down the \unknown\ you are looking for
e - write down the \equation(s)\ you will used based on the g and u
s - \substitute\ your numbers and compute the mathematical problem
s - find a \solution\ with appropriate units
solve for acceleration

1. a car starts from rest at a traffic light and accelerates uniformly to a speed of 20 m/s in 10 seconds. what is the cars acceleration?
2. a cyclist is moving at a speed of 5 m/s when they begin to pedal harder and increase their speed to 12 m/s over a period of 4 seconds. what is the acceleration of the cyclist?
3. an airplane accelerates down the runway, increasing its velocity from 15 m/s to 70 m/s in 30 seconds before takeoff. what is the airplanes acceleration?
4. a train is traveling at 40 m/s and applies its brakes, slowing down to 10 m/s in 15 seconds. what is the acceleration of the train as it decelerates?

solve for time

1. a sports car accelerates from 10 m/s to 50 m/s with an acceleration of 5 m/s². how much time does it take for the car?

Explanation:

Step1: Identify the acceleration formula

The formula for acceleration is $a=\frac{v - u}{t}$, where $v$ is final - velocity, $u$ is initial - velocity, and $t$ is time.

Step2: Solve problem 1

Given $u = 0\ m/s$ (starts from rest), $v = 20\ m/s$, $t = 10\ s$.
$a=\frac{v - u}{t}=\frac{20 - 0}{10}=2\ m/s^{2}$

Step3: Solve problem 2

Given $u = 5\ m/s$, $v = 12\ m/s$, $t = 4\ s$.
$a=\frac{v - u}{t}=\frac{12 - 5}{4}=1.75\ m/s^{2}$

Step4: Solve problem 3

Given $u = 15\ m/s$, $v = 70\ m/s$, $t = 30\ s$.
$a=\frac{v - u}{t}=\frac{70 - 15}{30}=\frac{55}{30}\approx1.83\ m/s^{2}$

Step5: Solve problem 4

Given $u = 40\ m/s$, $v = 10\ m/s$, $t = 15\ s$.
$a=\frac{v - u}{t}=\frac{10 - 40}{15}=\frac{- 30}{15}=-2\ m/s^{2}$

Step6: Solve problem 5

We use the formula $a=\frac{v - u}{t}$, and we need to solve for $t$. Rearranging gives $t=\frac{v - u}{a}$.
Given $u = 10\ m/s$, $v = 50\ m/s$, $a = 5\ m/s^{2}$.
$t=\frac{v - u}{a}=\frac{50 - 10}{5}=\frac{40}{5}=8\ s$

Answer:

1. $2\ m/s^{2}$
2. $1.75\ m/s^{2}$
3. $\approx1.83\ m/s^{2}$
4. $-2\ m/s^{2}$
5. $8\ s$