Question

practice: acceleration
answer the following questions. make sure to show all work to receive credit. you may need a separate sheet of paper.

1. a roller - coaster car rapidly picks up speed as it rolls down a hill. as it begins its descent, its speed is 4 m/s. 3 seconds later, at the bottom of the slope, its speed is 22 m/s. find its acceleration during this time.
2. a cyclist accelerates from 0 m/s to 8 m/s in 10 seconds. what is his acceleration?
3. a car approaches a stop sign going 6.0 m/s before it comes to a stop. if it does this in 4.2 seconds, what was its acceleration?
4. a car advertisement claims that a certain car can accelerate from rest to 76 km/hr in 7 seconds, or 0.0019 hours. find the car’s acceleration.
5. challenge: if a vehicle with an initial velocity of 15 m/s accelerates at a rate of 5 m/s² for 3 seconds, what will its final velocity be?

Explanation:

Step1: Recall acceleration formula

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

Step2: Solve problem 1

Given $u = 4$ m/s, $v=22$ m/s, $t = 3$ s. Substitute into the formula: $a=\frac{22 - 4}{3}=\frac{18}{3}=6$ m/s².

Step3: Solve problem 2

Given $u = 0$ m/s, $v = 8$ m/s, $t = 10$ s. Substitute into the formula: $a=\frac{8 - 0}{10}=0.8$ m/s².

Step4: Solve problem 3

Given $u = 6.0$ m/s, $v = 0$ m/s, $t = 4.2$ s. Substitute into the formula: $a=\frac{0 - 6.0}{4.2}=-\frac{6}{4.2}\approx - 1.43$ m/s².

Step5: Solve problem 4

First, convert $76$ km/hr to m/s. $76$ km/hr=$76\times\frac{1000}{3600}\approx21.11$ m/s, $u = 0$ m/s, $t = 7$ s. Substitute into the formula: $a=\frac{21.11 - 0}{7}\approx3.02$ m/s².

Step6: Solve problem 5

Use the formula $v=u+at$. Given $u = 15$ m/s, $a = 5$ m/s², $t = 3$ s. Substitute into the formula: $v=15+5\times3=15 + 15=30$ m/s.

Answer:

1. $6$ m/s²
2. $0.8$ m/s²
3. $-1.43$ m/s²
4. $3.02$ m/s²
5. $30$ m/s