Question

Two identical bus of size 6m are moving with velocity of 2m/s . Bus A decides to overtake Bus B. What should be the acceleration of bus A to overtake bus B in 3 seconds?

• A. 3.45 ${\text{ms}}^{-2}$
• B. 5.21 ${\text{ms}}^{-2}$
• C. 1.33 ${\text{ms}}^{-2}$
• D. 2.66 ${\text{ms}}^{-2}$

Answer 1

The correct option is D 2.66 ${\text{ms}}^{-2}$

Initial velocity of bus = 2 ${\text{ms}}^{-1}$
Time taken to overtake = 3 s
The Bus A will completely overtake when it crosses the bus B completely
Bus B moves $2\times 3$ = 6 m.
Distance to be covered to overtake = (6+6) + 6 = 18 m

s = ut + $\frac{1}{2}$ ${\text{at}}^2$
18 = 2 $\times$ 3 + $\frac{1}{2}$ (a) $\times$ 3 $\times$ 3
18 = 6 + $\frac{9}{2}$ a
$\frac{9}{2}$ a = 12
a = $\frac{24}{9}$
a = 2.66 ${\text{ms}}^{-2}$