Question

solving for other variables...
you can rearrange the acceleration equation to solve for initial speed, final speed, or time (as seen below).
initial speed = final speed - at final speed = at + initial speed
time = \\(\frac{\delta v}{a}\\)

1. how long will it take jesse with an acceleration of -3 m/s² to bring his skateboard with an initial speed of 13 m/s to a complete stop? (for this you are solving for time)

1. the elevators in the sears tower accelerate upward at 2.74 m/s² for 5 seconds to reach their final speed. if the elevators start at a speed of 0 m/s, what is their final speed? (for this you are solving for final speed)

1. a ball accelerating at 5.30 m/s² traveled for 11 seconds reaching a final velocity of 150 m/s. what was the ball’s initial speed? (here you are solving for initial speed)

Explanation:

Question 5

Step1: Identify known values

Final speed $v = 0\ \text{m/s}$ (complete stop), initial speed $u = 13\ \text{m/s}$, acceleration $a=- 3\ \text{m/s}^2$. The formula for time is $t=\frac{\Delta v}{a}$, where $\Delta v=v - u$.

Step2: Calculate $\Delta v$

$\Delta v=0 - 13=- 13\ \text{m/s}$

Step3: Calculate time

$t=\frac{\Delta v}{a}=\frac{- 13}{-3}=\frac{13}{3}\approx4.33\ \text{s}$

Question 6

Step1: Identify known values

Initial speed $u = 0\ \text{m/s}$, acceleration $a = 2.74\ \text{m/s}^2$, time $t = 5\ \text{s}$. The formula for final speed is $v=at + u$.

Step2: Substitute values into formula

$v=2.74\times5+0$

Step3: Calculate final speed

$v = 13.7\ \text{m/s}$

Question 7

Step1: Identify known values

Acceleration $a = 5.30\ \text{m/s}^2$, time $t = 11\ \text{s}$, final speed $v = 150\ \text{m/s}$. The formula for initial speed is $u=v - at$.

Step2: Substitute values into formula

$u = 150-5.30\times11$

Step3: Calculate initial speed

$u=150 - 58.3 = 91.7\ \text{m/s}$

Answer:

$\frac{13}{3}\ \text{s} \approx 4.33\ \text{s}$