a bus decreases its speed from 80 km per hour to 60 km per hour in 5 seconds find the acceleration of the bus
A bus decreases its speed from 80 km per hour to 60 km per hour in 5 seconds. Find the acceleration of the bus.
Answer: To find the acceleration of the bus, we need to follow these steps:
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Convert the speeds from km/h to m/s:
- Initial speed, u = 80 km/h
- Final speed, v = 60 km/h
To convert km/h to m/s, we use the conversion factor 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}.
So,
u = 80 \times \frac{1}{3.6} = \frac{80}{3.6} \approx 22.22 \text{ m/s}v = 60 \times \frac{1}{3.6} = \frac{60}{3.6} \approx 16.67 \text{ m/s}
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Use the formula for acceleration:
a = \frac{v - u}{t}
where:- a is the acceleration,
- v is the final velocity (16.67 m/s),
- u is the initial velocity (22.22 m/s),
- t is the time taken (5 seconds).
Plugging in the values, we get:
a = \frac{16.67 - 22.22}{5} -
Calculate the acceleration:
a = \frac{-5.55}{5} = -1.11 \text{ m/s}^2 ]
The negative sign indicates that the bus is decelerating. Therefore, the acceleration of the bus is -1.11 \text{ m/s}^2.