Question

A car accelerates uniformly from standstill to 60 mi/hr in 4s. What is its acceleration? How far does it travel during this time interval?

Answer 1

A car accelerates uniformly from standstill to $60\,\mathrm{mi/hr}$ in 4s. What is its acceleration? How far does it travel during this time interval?

Solution:

We write the general equation for the speed and the distance that depend on time.

$$\vec{v} = \vec{v_0} + \vec{a}t$$ $$\vec{r} = \vec{r_0} + \vec{v_0}t + \frac{\vec{a}t^2}{2}$$

In this case, the velocity and acceleration have the same direction.

Therefore, given that $v_0 = 0, r_0 = 0$

$$v = at, s = \frac{at^2}{2} \rightarrow a = \frac{v}{t} = \frac{60 \cdot \frac{1600\,m}{3600\,s}}{4\,s} = 6.67\, \frac{m^2}{s} \rightarrow s = \frac{6.67 \cdot 4^2}{2} = 53,36\,m$$

Answer: $a = 6.67\, \frac{m^2}{s}, s = 56.36\,m$