Question

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? 8. 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? 9. a car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. find the cars average acceleration. 10. a lizard accelerates from 2 m/s to 10 m/s in 4 seconds. what is the lizards average acceleration? 11. 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 runners acceleration in this part of the race? 12. 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 its 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. 13. a ball is dropped from the top of a building. after 2 seconds, its velocity is measured to be 19.6 m/s. calculate the acceleration for the dropped ball.

Explanation:

Step1: Recall acceleration formula

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

Step2: Solve problem 7

Given $u = 4\ m/s$, $v = 22\ m/s$, and $t = 3\ s$.
Substitute into the formula: $a=\frac{22 - 4}{3}=\frac{18}{3}=6\ m/s^{2}$.

Step3: Solve problem 8

Given $u = 0\ m/s$, $v = 8\ m/s$, and $t = 3\ s$.
Substitute into the formula: $a=\frac{8 - 0}{3}=\frac{8}{3}\approx2.67\ m/s^{2}$.

Step4: Solve problem 9

First, convert the velocities to SI units. $70\ km/h=\frac{70\times1000}{3600}\ m/s\approx19.44\ m/s$, $u = 0\ m/s$, and $t = 7\ s$.
Substitute into the formula: $a=\frac{19.44 - 0}{7}\approx2.78\ m/s^{2}$.

Step5: Solve problem 10

Given $u = 2\ m/s$, $v = 10\ m/s$, and $t = 4\ s$.
Substitute into the formula: $a=\frac{10 - 2}{4}=\frac{8}{4}=2\ m/s^{2}$.

Step6: Solve problem 11

Given $u = 5\ m/s$, $v = 9\ m/s$, and $t = 4\ s$.
Substitute into the formula: $a=\frac{9 - 5}{4}=\frac{4}{4}=1\ m/s^{2}$.

Step7: Solve problem 12

Given $u = 20\ m/s$, $v = 5\ m/s$, and $t = 2\ s$.
Substitute into the formula: $a=\frac{5 - 20}{2}=\frac{- 15}{2}=-7.5\ m/s^{2}$. The negative sign indicates deceleration.

Step8: Solve problem 13

Given $u = 0\ m/s$, $v = 19.6\ m/s$, and $t = 2\ s$.
Substitute into the formula: $a=\frac{19.6 - 0}{2}=9.8\ m/s^{2}$.

Answer:

Problem 7: $6\ m/s^{2}$
Problem 8: $\frac{8}{3}\ m/s^{2}\approx2.67\ m/s^{2}$
Problem 9: $\approx2.78\ m/s^{2}$
Problem 10: $2\ m/s^{2}$
Problem 11: $1\ m/s^{2}$
Problem 12: $-7.5\ m/s^{2}$
Problem 13: $9.8\ m/s^{2}$