Question

A bus is starting from rest and attains a velocity of 30 km/h in 15 sec. Find its acceleration

Answer 1

Answer:

${\bold{\therefore Acceleration=\frac{5}{9}m/s^{2}}}$

Explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a bus which is in rest and after 15 sec it attains a velocity of 30 km/h.

• So, we have to find the acceleration of the bus.

$\underline \bold{Given : } \\ \implies Initial \: velocity(u) = 0 \: m {s}^{ - 1} \\ \implies Final \: velocity(v) = 30 \: km {h}^{ - 1} \\ \implies Time(t) = 15 \: sec \\ \\ \underline \bold{To \: Find : } \\ \implies Acceleration(a) = ?$

• According to given question :

$\implies v = 30 \: km {h}^{ - 1} \times \frac{5}{18} \\ \implies v = \frac{25}{3} \: m {s}^{ - 1} \\ \bold{first \: method : } \\ \bold{By \: third \: equation \: of \: motion} \\ \implies s = ut + \frac{1}{2} a {t}^{2} \\ \implies s = 0 \times 15 + \frac{1}{2} \times a \times {15}^{2} \\ \bold{\implies s = \frac{225a}{2}} - - - - - (1) \\ \bold {By \: second\: equation \: of \: motion} \\ \implies {v}^{2} = {u}^{2} + 2as - - - - - (2) \\ \bold{putting \: value \: of \: s \: in \: (2)} \\ \implies { (\frac{25}{3}) }^{2} = {0}^{2} + 2 \times a \times \frac{225a}{2} \\ \implies \frac{625}{9} = 225 ({a})^{2} \\ \implies {a}^{2} = \frac{625}{9 \times 225} \\ \implies {a}^{2} = \frac{25}{81} \\ \implies a = ({ \frac{25}{81} })^{2} \\ \bold{\implies a = \frac{5}{9} m/ {s}^{2} }$

$\bold{alternate \: method : } \\ \implies v = \frac{25}{3} \: m {s}^{ - 1} \\ \\ \bold{by \: first \: equation \: of \: motion : } \\ \implies v = u + at \\ \implies \frac{25}{3} = 0 + a \times 15 \\ \implies 15 \times a = \frac{25}{3} \\ \implies a = \frac{25}{3 \times 15} \\ \bold{\implies a = \frac{5}{9} {ms}^{ - 2} }$

Answer 2

ANSWER:-

Given:

A bus is starting from rest and attains a velocity of 30km/hr in 15 second.

To find:

Find it's acceleration.

Solution:

⏺️Initial value,(u)= 0 m/sec.

⏺️Final value, (v)= 30km/hr

⏺️Time, (t)= 15sec.

From final velocity:

1km= 1000m

30km= 30× 1000= 30000m

1hr.= 60minutes

1 minutes= 60 second

=) 60×60

=) 3600 seconds

Final value= 30000/3600

=) 25/3 m/sec.

Now,

According to the first equation of motion:

=) v= u + at

=) 25/3= 0 + a×15

=) 25/3 = 15a

=) 25 = 45a

=) a= 25/45

=) a= 5/9m/s²

Hence,

Acceleration is 5/9 m/s².

Hope it helps ☺️