when the shuttle bus comes to a sudden stop to avoid hitting a dog, it decelerates uniformly at 4.7m/s as it slows from 8.7 m/s to 0 m/s. find the time interval of acceleration for the bus
To find the time interval of acceleration for the bus, we need to determine the time it takes for the bus to decelerate from 8.7 m/s to 0 m/s.
First, we need to calculate the acceleration of the bus using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 8.7 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -4.7 m/s² (negative because it's decelerating)
Using the formula, we have:
-4.7 = (0 - 8.7) / time
Simplifying the equation, we get:
-4.7 = -8.7 / time
To isolate the variable "time," we can cross-multiply and divide:
-8.7 × time = -4.7
time = -4.7 / -8.7
time ≈ 0.5402 seconds
Therefore, the time interval of acceleration for the bus is approximately 0.5402 seconds.