Question

name:
quiz 5 - using the constant acceleration formulas (/11)
show all of your work.

1. a car, with a starting velocity of 10m/s accelerates to 35m/s over a period of 10s. using only a velocity/time graph (do not use formulas from the formula sheet), calculate the displacement of the car over the time interval. (4)

$overrightarrow{v_{i}} = 10m/s$
$overrightarrow{v_{f}} = 35m/s$
$delta t = 10s$

1. a car is travelling with a velocity of 20m/s. the driver increases the cars speed at a rate of 0.5m/s² until the cars velocity is 25m/s. for how long, in seconds, was the car accelerating to reach the new speed of 25m/s? (3)

equation
$delta overrightarrow{d} = (\frac{\overrightarrow{v_{f}} + \overrightarrow{v_{i}}}{2}) delta t$
$\overrightarrow{v_{f}} = \overrightarrow{v_{i}} + \overrightarrow{a_{av}} delta t$
$delta overrightarrow{d} = \overrightarrow{v_{i}} delta t + \frac{1}{2} \overrightarrow{a_{av}} delta t^{2}$
$v_{f}^{2} = v_{i}^{2} + 2a_{av} delta d$
$delta overrightarrow{d} = \overrightarrow{v_{f}} delta t - \frac{1}{2} \overrightarrow{a_{av}} delta t^{2}$

Explanation:

Step1: Identify the formula

We use the formula \(v_{f}=v_{i}+a_{av}\Delta t\). Here, \(v_{i} = 20m/s\), \(v_{f}=25m/s\), \(a_{av}=0.5m/s^{2}\), and we need to find \(\Delta t\).

Step2: Rearrange the formula for \(\Delta t\)

From \(v_{f}=v_{i}+a_{av}\Delta t\), we can get \(\Delta t=\frac{v_{f}-v_{i}}{a_{av}}\).

Step3: Substitute the values

Substitute \(v_{i} = 20m/s\), \(v_{f}=25m/s\), \(a_{av}=0.5m/s^{2}\) into \(\Delta t=\frac{v_{f}-v_{i}}{a_{av}}\). So \(\Delta t=\frac{25 - 20}{0.5}\).

Step4: Calculate the result

\(\Delta t=\frac{5}{0.5}=10s\).

Answer:

The car was accelerating for \(10s\).