Question

A bus was moving with a speed of 54 km/h. On applying brakes,it stopped in 8 seconds. Calculate the speed acquired and the distance travelled in this time.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Final\:velocity=0\:m/s}}}$

$\green{\tt{\therefore{Distance\:travel=60\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Initial \: velocity = 54 \: km/h\\ \\ \tt:\implies Time(t)=8\:sec \\ \red{\underline \bold{To \: Find:}} \\\\ \tt: \implies Final\:velocity= ?\\ \\ \tt: \implies Distance \: travel \: in \: that \: time =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt \circ \: For \: stopping \: bus - - - - \\ \\ \green{\tt: \implies Final \: velocity = 0 \: m/s }\\ \\ \tt \circ \: Initial \: velocity = 54 \times \frac{5}{18} = 15 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 0 = 15 + a \times 8 \\ \\\tt: \implies - 15 = a \times 8 \\ \\ \green{\tt: \implies a = \frac{ - 15}{8} \: m/s} \\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies s = ut + \frac{1}{2} {at}^{2} \\ \\ \tt: \implies s = 15 \times 8 + \frac{1}{2} \times \frac{ - 15}{8} \times {8}^{2} \\ \\ \tt: \implies s =120 - 60 \\ \\ \green{\tt: \implies s =60 \: m}$

Answer 2

Given :-

• A bus was moving with a speed of 54 km/h.

• On applying brakes, it stopped in 8 seconds.

To Find :-

The speed acquired and the distance travelled in that time.

Solution :-

Initial velocity(u) = 54 km/h = 54 × (5/18) = 15 m/s

Final velocity(v) = 0 m/s         ( ...As the bus came to rest at last)

Time(t) = 8 secs

We know,

$\sf{v=u+at}$

Putting the given values :-

0 = 15 + a(8)

⇒ -15 = 8a

⇒ a = -15/8

We also know,

$\italics{\sf{s=ut+\frac{1}{2}at^2 }}$

Putting the given values :-

$\sf{s=15(8)+\frac{1}{2}\times\frac{-15}{8}\times(8)^2 }\\\\\sf{\implies s=120-\frac{15}{2}\times 8 }\\\\\sf{\implies s=120-60}\\\\\boxed{\sf{\implies s=60\ m}}$

⇒ So, the acquired speed = Distance/time = 60/8 = 7.5 m/s.

⇒ Distance travelled = 60 m.