Question

bus has a uniform acceleration of 6 m/s2. What distance will it cover in 10 s after start?​

Answer 1

Explanation:

u = 0 m/s

a = 6 m/ s²

t = 10 s

S = ut +1/2 × at²

0×10 + 1/2 × 6×10²

0 +300

S = 300 m

Hence, distance cover by bus after 10 sec is 300 m

Answer 2

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to find out the distance. If a bus is uniformly accelerated that is of 6 m/s² Time taken by the bus is 10 seconds.

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

$\sf Given \begin{cases} & \sf{Initial \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Acceleration \: = \bf{6 \: m/s^{2}}} \\ \\ & \sf{Time \: = \bf{10 \: seconds}} \\ \\ & \sf{Distance \: = \bf{?}} \end{cases}$

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Second equation of motion that is given by

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{s \: = ut + \dfrac{1}{2} \times at^{2}}}}}}$

(Where, s denotes displacement or distance , u denotes initial velocity , v denotes final velocity , ½ means half and a denotes acceleration)

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

$:\implies \sf s \: = ut + \dfrac{1}{2} \times at^{2} \\ \\ :\implies \sf s \: = 0(10) + \dfrac{1}{2} \times 6(10)(10) \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 6(100) \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 600 \\ \\ :\implies \sf s \: = \dfrac{600}{2} \\ \\ :\implies \sf s \: = \cancel{\dfrac{600}{2}} \: (Cancelling) \\ \\ :\implies \sf s \: = 300 \: metres \\ \\ :\implies \sf Distance \: = 300 \: metres$

Henceforth, the distance is 300 m

${\bigstar \:{\pmb{\sf{\underline{Additional \: knowledge...}}}}}$

⋆ Acceleration: The term acceleration is a measure of the change in the velocity of an object per unit time.

So, according to the question we have to find out the change in velocity of the object that is acceleration.

${\small{\underline{\boxed{\sf{Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken}}}}}}$

• If the velocity of an object is changes from initial value u to the final value v in the time t the acceleration a be

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

The SI unit of acceleration is m/s²