Question

1. a car advertisement claims that a certain car can accelerate from rest to 70 km/hr in 7 seconds (hint: convert to hours first!) find the cars acceleration

Explanation:

Step1: Convert final velocity to m/s

The final velocity $v = 70\ km/h$. To convert it to m/s, we use the conversion factor: $1\ km = 1000\ m$ and $1\ h=3600\ s$. So $v = 70\times\frac{1000}{3600}\ m/s=\frac{70000}{3600}\ m/s=\frac{175}{9}\ m/s\approx19.44\ m/s$. The initial velocity $u = 0\ m/s$ (starts from rest) and time $t = 7\ s$.

Step2: Use the acceleration formula

The acceleration formula is $a=\frac{v - u}{t}$. Substituting the values $u = 0\ m/s$, $v=\frac{175}{9}\ m/s$ and $t = 7\ s$ into the formula, we get $a=\frac{\frac{175}{9}-0}{7}=\frac{175}{9\times7}=\frac{25}{9}\ m/s^{2}\approx2.78\ m/s^{2}$.

Answer:

$\frac{25}{9}\ m/s^{2}\approx2.78\ m/s^{2}$