a bus decreases its speed from 80 km per hour to 60 km per hour in 5 seconds find the acceleration of the bus
What is the acceleration of the bus?
Answer:
To find the acceleration of the bus, we can use the formula for acceleration:
[ a = \frac{\Delta v}{\Delta t} ]
Where:
- ( a ) is the acceleration,
- ( \Delta v ) is the change in velocity,
- ( \Delta t ) is the change in time.
In this case, the bus decreases its speed from 80 km/h to 60 km/h in 5 seconds. We first need to find the change in velocity:
[ \Delta v = v_f - v_i ]
Where:
- ( v_f ) is the final velocity,
- ( v_i ) is the initial velocity.
Given that the initial velocity ( v_i = 80 ) km/h and the final velocity ( v_f = 60 ) km/h, we can calculate the change in velocity:
[ \Delta v = 60 , \text{km/h} - 80 , \text{km/h} = -20 , \text{km/h} ]
Since the velocity decreases, we have a negative change in velocity. However, in calculations, we consider magnitudes, so we take the absolute value:
[ |\Delta v| = |-20 , \text{km/h}| = 20 , \text{km/h} ]
Now, we can use the formula for acceleration:
[ a = \frac{\Delta v}{\Delta t} ]
Given that ( \Delta v = 20 ) km/h and ( \Delta t = 5 ) seconds, let’s convert the units to be consistent. Since 1 hour is equal to 3600 seconds:
[ 20 , \text{km/h} = \frac{20 , \text{km}}{3600 , \text{s/h}} = \frac{1}{180} , \text{km/s} ]
Now, we can calculate the acceleration:
[ a = \frac{\frac{1}{180} , \text{km/s}}{5 , \text{s}} = \frac{1}{900} , \text{km/s}^2 ]
Therefore, the acceleration of the bus is ( \frac{1}{900} , \text{km/s}^2 ), which means the speed of the bus decreases by ( \frac{1}{900} ) kilometers per second squared.