Question

unit 1 - speed and acceleration practice problems
directions: answer the following speed and acceleration problems using the circle diagram. for each calculation, show your work and write the answer with appropriate si units.

1. during a race, a sprinter runs at a speed of 6 m/s. 2 seconds later, she is running at a speed of 10 m/s. what is the runners acceleration? show your work.

equation | circle diagram | givens | work | answer w/si units

1. if you ride your bike at an average speed of 4 km/h and need to travel a total distance of 28 km, how long will it take you to reach your destination? show your work.

equation | circle diagram | givens | work | answer w/si units

1. what is the acceleration of a car that goes from 20 km/h to 100 km/h in 2 hours?

equation | circle diagram | givens | work | answer w/si units

1. an object traveling at 80 m/s takes 15 s to come to a stop, what is its acceleration?

equation | circle diagram | givens | work | answer w/si units

Explanation:

1.

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.
$a=\frac{v - u}{t}$

Step2: Identify the given values

$u = 6\ m/s$, $v = 10\ m/s$, $t = 2\ s$

Step3: Substitute values into the formula

$a=\frac{10 - 6}{2}=\frac{4}{2}=2\ m/s^{2}$

Step1: Identify the time - distance - speed formula

The formula for time is $t=\frac{d}{s}$, where $d$ is distance and $s$ is speed.
$t=\frac{d}{s}$

Step2: Identify the given values

$d = 28\ km$, $s = 4\ km/h$

Step3: Substitute values into the formula

$t=\frac{28}{4}=7\ h$

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. First, convert velocities to SI units. $20\ km/h=\frac{20\times1000}{3600}\ m/s=\frac{50}{9}\ m/s\approx5.56\ m/s$, $100\ km/h=\frac{100\times1000}{3600}\ m/s=\frac{250}{9}\ m/s\approx27.78\ m/s$, $t = 2\ h=2\times3600\ s = 7200\ s$
$a=\frac{v - u}{t}$

Step2: Substitute values into the formula

$a=\frac{\frac{250}{9}-\frac{50}{9}}{7200}=\frac{\frac{200}{9}}{7200}=\frac{200}{9\times7200}=\frac{1}{324}\ m/s^{2}\approx0.0031\ m/s^{2}$

Answer:

$2\ m/s^{2}$

2.