Question

A need good answer with proper explanation :-

A decreases its speed from 80 km/h to 60 km/h in 5 second. Find the acceleration of the bus.

[ kindly multiply 5/8 to the value for converting them into m/s ]

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Answer 1

ANSWER:

• The acceleration of the bus = - 1.11 m/s².

GIVEN:

• A bus decreases its speed from 80 kmph to 60 kmph in 5 s.

TO FIND

• The acceleration of the bus.

CONVERSIONS:

• 1 kmph = 1000/3600 m/s

• 1 kmph = 10 / 36 m/s

• 1 kmph = 5/18 m/s.

EXPLANATION:

80 kmph = 80 × 5/18 m/s

80 kmph = 40 × 5/9 m/s

80 kmph = 200/9 m/s

60 kmph = 60 × 5/18 m/s

60 kmph = 30 × 5/9 m/s

60 kmph = 150/9 m/s

$\boxed{\bold{\large{\gray{Acceleration = \dfrac{v-u}{t}}}}}$

v = 150/9 m/s

u = 200/9 m/s

t = 5 s

$\sf Acceleration = \dfrac{ \dfrac{150}{9} - \dfrac{200}{9} }{5}$

$\sf Acceleration = \dfrac{ \dfrac{150 - 200}{9} }{5}$

$\sf Acceleration = \dfrac{ - 50}{45}$

$\sf Acceleration = -1.11 \ m {s}^{ - 2}$

Hence the acceleration of the bus = - 1.11 m/s².

EXTRA CALCULATIONS:

Force exerted by the bus = Ma [ where M is the mass of the bus ]

$\boxed{\bold{\large{\gray{a = \dfrac{v-u}{t}}}}}$

$\sf F = \dfrac{M(v-u)}{t}$

$\sf F = M( -1.11)$

$\sf F = -1.11M\ newton$

$\boxed{\bold{\large{\gray{Momentum = M(v - u)}}}}$

$\sf v - u = \dfrac{ 150}{9} - \dfrac{200}{9}$

$\sf v - u = \dfrac{ 150 - 200}{9}$

$\sf v - u = \dfrac{ - 50 }{9}$

$\sf v - u = - 5.56$

$\sf p= m(v - u) = M( - 5.56) \ kgm {s}^{ - 1}$

$\sf p=- 5.56M \ kgm {s}^{ - 1}$