Question

acceleration calculations

1. a girl rode her skateboard at 4 m/s. when she turned the corner she started going downhill at 8 m/s for 10 seconds. what was her acceleration?
2. a bowling ball is dropped from the top of the building. after 5 seconds, its velocity is 47 m/s. what is its acceleration?
3. a horse fell jumping over a hurdle. he got up and after 5 seconds returned to a velocity of 10 m/s. what is his acceleration?
4. wind was blowing a shopping cart making it roll 6 m/s. it hit a garbage bin and rolled to a stop. this took 8 seconds. what was its acceleration?

final velocity m\tinitial velocity m\t vf - vi δv\ttime s\t a = \frac{δv}{t}

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 1

Initial velocity $v_i = 4$ m/s, final velocity $v_f=8$ m/s, time $t = 10$ s.
$a=\frac{8 - 4}{10}=\frac{4}{10}=0.4$ m/s²

Step3: Solve problem 2

Initial velocity $v_i = 0$ m/s (dropped), final velocity $v_f = 47$ m/s, time $t = 5$ s.
$a=\frac{47-0}{5}=\frac{47}{5}=9.4$ m/s²

Step4: Solve problem 3

Initial velocity $v_i = 0$ m/s (just got up), final velocity $v_f = 10$ m/s, time $t = 5$ s.
$a=\frac{10 - 0}{5}=\frac{10}{5}=2$ m/s²

Step5: Solve problem 4

Initial velocity $v_i = 6$ m/s, final velocity $v_f = 0$ m/s (stopped), time $t = 8$ s.
$a=\frac{0 - 6}{8}=\frac{-6}{8}=- 0.75$ m/s²

Final velocity (m/s)	Initial velocity (m/s)	$v_f - v_i$ (m/s)	Time (s)	$a=\frac{v_f - v_i}{t}$ (m/s²)
47	0	47	5	9.4
10	0	10	5	2
0	6	-6	8	-0.75

Answer:

Final velocity (m/s)	Initial velocity (m/s)	$v_f - v_i$ (m/s)	Time (s)	$a=\frac{v_f - v_i}{t}$ (m/s²)
47	0	47	5	9.4
10	0	10	5	2
0	6	-6	8	-0.75