Question

1. a car accelerates from 20 km/hr to 80 km/hr in 2 hours. what is its acceleration?
2. a man starts jogging at a rate of 33 m/min and after jogging for 15 mins, he runs into a neighbor and slows to 5 m/min to say hello. what is his acceleration (or deceleration)?
3. a ball is dropped off a cliff and hits the ground in 10 seconds. what was the distance the ball fell?
4. what is the velocity of a free - falling apple that took 5 seconds to fall?
5. a person spat out their gum on the roof of a building and fell for 3 seconds. how far did it fall?
6. what is the velocity of a free - falling tennis ball that falls for 9 seconds?

Explanation:

Step1: Recall 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: Identify values for car problem

For the car, $v_i = 20$ km/hr, $v_f=80$ km/hr, and $t = 2$ hours.

Step3: Calculate acceleration of the car

$a=\frac{80 - 20}{2}=\frac{60}{2}=30$ km/hr².

Step4: Identify values for jogger problem

For the jogger, $v_i = 33$ m/min, $v_f = 5$ m/min, and $t = 15$ min.

Step5: Calculate acceleration of the jogger

$a=\frac{5 - 33}{15}=\frac{- 28}{15}\approx - 1.87$ m/min².

Step6: Recall free - fall distance formula

The formula for the distance of a free - falling object is $d=\frac{1}{2}gt^{2}$, where $g$ is the acceleration due to gravity ($g = 10$ m/s²) and $t$ is time.

Step7: Calculate distance the ball fell

For the ball dropped off a cliff with $t = 10$ s, $d=\frac{1}{2}\times10\times10^{2}=5\times100 = 500$ m.

Step8: Recall free - fall velocity formula

The formula for the velocity of a free - falling object is $v = gt$.

Step9: Calculate velocity of the free - falling apple

For the apple with $t = 5$ s, $v=10\times5 = 50$ m/s.

Step10: Calculate distance the gum fell

For the gum with $t = 3$ s, $d=\frac{1}{2}\times10\times3^{2}=5\times9 = 45$ m.

Step11: Calculate velocity of the free - falling tennis ball

For the tennis ball with $t = 9$ s, $v=10\times9 = 90$ m/s.

Answer:

1. $30$ km/hr²
2. $-\frac{28}{15}\approx - 1.87$ m/min²
3. $500$ m
4. $50$ m/s
5. $45$ m
6. $90$ m/s