Question

acceleration practice problems
acceleration = \frac{finalvelocity - initialvelocity}{time}
you must show your work.
you can use a calculator but you must show all of the steps involved in doing the problem.
short answer

1. does the speedometer of a car read average speed or instantaneous speed? how do you know?
2. if the speedometer of your car reads a constant speed of 40km/hr, can you say 100% for sure that the car has a constant velocity? explain your answer.
3. what two controls on a car cause a change in speed?
4. what control causes a change in velocity?
5. what is the acceleration of a car that travels in a straight line at a constant speed?
6. describe a situation in which you can accelerate even though your speed doesn’t change.

calculations

1. a roller coaster car rapidly picks up speed as it rolls down a slope. as it starts down the slope, its speed is 4 m/s. but 3 seconds later, at the bottom of the slope, its speed is 22 m/s. what is its average acceleration?
2. a cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. what is his acceleration? is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds?
3. a car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. find the car’s average acceleration.
4. a lizard accelerates from 2 m/s to 10 m/s in 4 seconds. what is the lizard’s average acceleration?
5. a runner covers the last straight stretch of a race in 4 s. during that time, he speeds up from 5 m/s to 9 m/s. what is the runner’s acceleration in this part of the race?
6. you are traveling in a car that is moving at a velocity of 20 m/s. suddenly, a car 10 meters in front of you slams on it’s brakes. at that moment, you also slam on your brakes and slow to 5 m/s. calculate the acceleration if it took 2 seconds to slow your car down.
7. a ball is dropped from the top of a building. after 2 seconds, it’s velocity is measured to be 19.6 m/s. calculate the acceleration for the dropped ball.

Explanation:

Step1: Identify the acceleration formula

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

Step2: Solve problem 7

Given $v_i = 4\ m/s$, $v_f=22\ m/s$, and $t = 3\ s$.
$a=\frac{22 - 4}{3}=\frac{18}{3}=6\ m/s^2$

Step3: Solve problem 8

For the cyclist: $v_i = 0\ m/s$, $v_f = 8\ m/s$, $t = 3\ s$.
$a_{cyclist}=\frac{8 - 0}{3}=\frac{8}{3}\approx2.67\ m/s^2$
For the car: $v_i = 0\ m/s$, $v_f = 30\ m/s$, $t = 8\ s$.
$a_{car}=\frac{30 - 0}{8}=\frac{30}{8}=3.75\ m/s^2$
Since $\frac{8}{3}\approx2.67<3.75$, the car's acceleration is higher.

Step4: Solve problem 9

First, convert $70\ km/h$ to $m/s$.
$70\ km/h=\frac{70\times1000}{3600}\ m/s\approx19.44\ m/s$
$v_i = 0\ m/s$, $v_f\approx19.44\ m/s$, $t = 7\ s$.
$a=\frac{19.44 - 0}{7}\approx2.78\ m/s^2$

Step5: Solve problem 10

Given $v_i = 2\ m/s$, $v_f = 10\ m/s$, $t = 4\ s$.
$a=\frac{10 - 2}{4}=\frac{8}{4}=2\ m/s^2$

Step6: Solve problem 11

Given $v_i = 5\ m/s$, $v_f = 9\ m/s$, $t = 4\ s$.
$a=\frac{9 - 5}{4}=\frac{4}{4}=1\ m/s^2$

Step7: Solve problem 12

Given $v_i = 20\ m/s$, $v_f = 5\ m/s$, $t = 2\ s$.
$a=\frac{5 - 20}{2}=\frac{- 15}{2}=-7.5\ m/s^2$

Step8: Solve problem 13

Given $v_i = 0\ m/s$, $v_f = 19.6\ m/s$, $t = 2\ s$.
$a=\frac{19.6 - 0}{2}=9.8\ m/s^2$

Answer:

s:

1. $6\ m/s^2$
2. Cyclist's acceleration: $\frac{8}{3}\ m/s^2\approx2.67\ m/s^2$, Car's acceleration is higher.
3. $\approx2.78\ m/s^2$
4. $2\ m/s^2$
5. $1\ m/s^2$
6. $-7.5\ m/s^2$
7. $9.8\ m/s^2$