A bus accelerates uniformly from 8 M/s to 24 m/s in 4 seconds. What is the acceleration produced? Also calculate the distance covered by the bus during the given time?
a = change in speed/ time = 16/4 = 4 m/s^2
average speed = (8 + 24)/2 = 16 m/s
so distance = 16 * 4 = 64 meters
To find the acceleration of the bus, we can use the formula:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Given:
Initial Velocity (u) = 8 m/s
Final Velocity (v) = 24 m/s
Time (t) = 4 seconds
Substituting the given values into the formula:
Acceleration (a) = (24 m/s - 8 m/s) / 4 seconds
Acceleration (a) = 16 m/s / 4 seconds
Acceleration (a) = 4 m/s²
Therefore, the acceleration produced by the bus is 4 m/s².
To calculate the distance covered by the bus during the given time, we can use the formula:
Distance (s) = Initial Velocity × Time + (1/2) × Acceleration × Time²
Given:
Initial Velocity (u) = 8 m/s
Time (t) = 4 seconds
Acceleration (a) = 4 m/s²
Substituting the given values into the formula:
Distance (s) = 8 m/s × 4 seconds + (1/2) × 4 m/s² × (4 seconds)²
Distance (s) = 32 m + (1/2) × 4 m/s² × 16 seconds²
Distance (s) = 32 m + 32 m
Distance (s) = 64 meters
Therefore, the bus covers a distance of 64 meters during the given time.
To find the acceleration produced by the bus, we can use the formula:
acceleration = (change in velocity) / time
In this case, the change in velocity is:
change in velocity = final velocity - initial velocity
change in velocity = 24 m/s - 8 m/s
change in velocity = 16 m/s
The time is given as 4 seconds.
Now we can calculate the acceleration:
acceleration = (change in velocity) / time
acceleration = 16 m/s / 4 s
acceleration = 4 m/s²
Therefore, the acceleration produced by the bus is 4 m/s².
To calculate the distance covered by the bus during the given time, we can use another formula:
distance = initial velocity * time + (1/2) * acceleration * time²
The initial velocity is 8 m/s, the time is 4 seconds, and the acceleration is 4 m/s².
distance = 8 m/s * 4 s + (1/2) * 4 m/s² * (4 s)²
distance = 32 m + 0.5 * 4 m/s² * 16 s²
distance = 32 m + 0.5 * 64 m
distance = 32 m + 32 m
distance = 64 m
Therefore, the distance covered by the bus during the given time is 64 meters.