A car starting from rest accelerates uniformly to acquire a speed 20 km h^-1 in 30 min. The distance travelled by car in this time interval will be —

1. 600 km
2. 5 km
3. 6 km
4. 10 km

5 km

Reason —

As we know,

v = u + at

Given,

u = 0

v = 20 km h^-1

t = 30 min = $\dfrac{1}{2}$ h

Substituting the values in the formula above, we get,

$20 = 0 + (a \times \dfrac{1}{2}) \\[0.5em] \Rightarrow a = 40 \text{ km h}^{-2} \\[0.5em]$

Now,

S = ut + $\dfrac{1}{2}$ at²

Substituting the values in the formula above we get,

$\text{S} = (0 \times 0.5) + \Big[\dfrac{1}{2} \times 40 \times \Big(\dfrac{1}{2}\Big)^2\Big] \\[0.5em] \text{S} = 0 + \Big(\dfrac{1}{2} \times 40 \times \dfrac{1}{4}\Big) \\[0.5em] \Rightarrow \text{S} = 5 \text{ km} \\[0.5em]$

Hence, distance = 5 km