1. Let the maximum speed be $v = 80\ \text{km/h}$

2. First part: uniform acceleration from rest to $80$ km/h in time $t$

   For uniformly accelerated motion, average speed in this interval is $\frac{u+v}{2} = \frac{0+80}{2} = 40\ \text{km/h}$

   Hence distance covered in first part is $s_1 = 40\times t$

3. Second part: constant speed for time $3t$

   Speed is constant at $80$ km/h, so distance covered is $s_2 = 80\times 3t = 240t$

4. Total distance and total time

   Total distance: $s = s_1+s_2 = 40t+240t = 280t$

   Total time: $T = t+3t = 4t$

5. Average speed

   $v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} = \frac{280t}{4t} = 70\ \text{km/h}$

6. Check options

   • A: $70$ ✅
   • B: $40$ ❌
   • C: $30$ ❌
   • D: $80$ ❌

Therefore, the correct answer is A.