Question

A certain car is capable of accelerating at a rate of 0.53 m/s2. How long does it take for this car to go from a speed of 30 mi/h to a speed of 32 mi/h?

Answer 1

Task. A certain car is capable of accelerating at a rate of $a=0.53\,m/s^{2}$. How long does it take for this car to go from a speed of $v_{0}=30\,mi/h$ to a speed of $v_{1}=32\,mi/h$?

Solution. Recall that one mile is equal to 1609 $m$, so

$1\ mi/h=\frac{1609\ m}{3600\ s}=0.447m/s.$

Since the acceleration of the car is constant, the relation between velocity and time is given by the following formula:

$v(t)=v_{0}+at.$

We should find $\bar{t}$ such that $v(\bar{t})=v_{1}$, so

$v_{1}=v_{0}+a\bar{t},$

whence

$\bar{t}=\frac{v_{1}-v_{0}}{a}.$

Substituting values we obtain

$\bar{t}=\frac{v_{1}-v_{0}}{a}=\frac{(32-30)\ mi/h}{0.53\ m/s^{2}}=\frac{2*0.447m/s}{0.53\ m/s^{2}}=1.69\ s.$

Answer. 1.69 s.