Question

A bus starting from rest moves with a uniform acceleration of 0.1 m/s^2 for3 minutes. Find the speed acquired and the distance travelled? *
2

Answer 1

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

$\green{\tt{\therefore{Distance=1620\:m}}}$

$\green{\tt{\therefore{Final\:velocity=18\:m/s}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Acceleration(a) = 0.1 { \: m/s}^{2} \\ \\ \tt: \implies Time(t) = 3 \: min \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Distance \: travelled =? \\ \\ \tt: \implies Final \: velocity =?$

• According to given question :

$\tt \circ \: Initial \: speed = 0 \: {m/s}^{2} \\ \\ \tt \circ \: Time = 3 \times 60 = 180 \: sec\\ \\ \bold{As \: we \:know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies v = 0 +0.1 \times 180 \\ \\ \green{\tt: \implies v = 18 \: m/s} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {18}^{2} = {0}^{2} + 2 \times 0.1 \times s \\ \\ \tt: \implies 324 = 0.2 \times s \\ \\ \tt: \implies s = \frac{324}{0.2} \\ \\ \green{\tt: \implies s = 1620 \: m}$

Answer 2

Given:-

• Initial velocity of bus (u) = 0m/s

• Acceleration of bus (a) = 0.1m/s²

• Time taken (t) = 3min = 3×60=180s

To Find:-

• Final velocity of bus (v).

• Distance covered by bus (s)

Solution:-

By using 1st equation of motion

✧ v = u +at

Put the values which is given above

⟹ v = 0+0.1 ×180

⟹ v = 18m/s

∴ The Final velocity of the bus is 18m/s

And Now, we have to calculate the distance traveled by bus. So,

By using 2nd equation of motion

⟹s = ut +1/2at²

Put the value which is given above

⟹ s = 0×180+1/2×0.1 ×180²

⟹ s = 0+1/2 × 0.1×32400

⟹ s = 1/2 ×3240

⟹s = 1620m or 1.62 Km

∴ Distance covered by bus is 1620m or 1.62km.

Additional Information!!

Some equation of motion are

⟹ v = u +at

⟹s = ut +1/2at².

⟹ v² = u² + 2as

Here,

v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement or Distance

t is the time taken