Question

1. a motorcycle drives 30 km n and then travels 20 km s in 0.5 hours. 4 marks

a) what is the motorcycles average speed?

1. in an acceleration test for high end sports cars, two markers are placed 300 m apart on a long straight road. a ferrari passed the first marker with a velocity of 5.0 m/s e and passed the second marker with a velocity of 33 m/s e. calculate the ferrari’s acceleration between the two markers. 4 marks

Explanation:

1.

Step1: Calculate total distance

The motorcycle travels 30 km north and 20 km south. The total distance \(d\) is the sum of the magnitudes of the distances traveled. \(d = 30+20=50\) km.

Step2: Calculate total time

The total time \(t = 0.5\) hours.

Step3: Calculate average speed

The formula for average speed \(v_{avg}=\frac{d}{t}\). Substituting the values, we get \(v_{avg}=\frac{50}{0.5}=100\) km/h.

Step1: Identify given values

The initial velocity \(u = 5.0\) m/s, the final velocity \(v = 33\) m/s, and the displacement \(s=300\) m.

Step2: Use the equation \(v^{2}=u^{2}+2as\)

We want to find the acceleration \(a\). Rearranging the equation \(v^{2}=u^{2}+2as\) for \(a\), we get \(a=\frac{v^{2}-u^{2}}{2s}\).

Step3: Substitute values

\[

$$\begin{align*} a&=\frac{33^{2}-5.0^{2}}{2\times300}\\ &=\frac{(33 + 5)(33 - 5)}{600}\\ &=\frac{38\times28}{600}\\ &=\frac{1064}{600}\\ &\approx1.77\ m/s^{2} \end{align*}$$

\]

Answer:

100 km/h

2.