A car moves with uniformly velocity of 12m/s for 6s.After this it accelerates at 2m/s2 for 4s.it travels for 2 more second with uniform velocity. the car finally accelerates to a stop in 15s .calculate (a)the distance travelled in 5 second (b)average velocity for the journey was in a straight line
To calculate the distance traveled in 5 seconds, we need to break down the motion of the car into different parts and calculate the distance for each part separately.
Given:
Initial velocity (uniform): 12 m/s
Duration of uniform velocity: 6 seconds
Acceleration: 2 m/s²
Duration of acceleration: 4 seconds
Total time: 15 seconds
(a) Distance traveled in 5 seconds:
Step 1: Distance traveled during the uniform velocity period of 6 seconds.
In this period, the car moves with a constant velocity of 12 m/s. The formula to calculate distance when velocity is constant is:
Distance = Velocity × Time
Substituting the given values:
Distance = 12 m/s × 6 s
Distance = 72 meters
Step 2: Distance traveled during the acceleration period of 4 seconds.
Using the formula for distance when acceleration is involved:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time²
Substituting the given values:
Distance = 12 m/s × 4 s + (1/2) × 2 m/s² × (4 s)²
Distance = 48 meters + 16 meters
Distance = 64 meters
Step 3: Distance traveled during the second period of uniform velocity for 2 seconds.
Again, we use the formula for distance when velocity is constant:
Distance = Velocity × Time
Substituting the given values:
Distance = 12 m/s × 2 s
Distance = 24 meters
Therefore, the total distance traveled in 5 seconds is:
Total Distance = Distance during uniform velocity + Distance during acceleration + Distance during uniform velocity
Total Distance = 72 meters + 64 meters + 24 meters
Total Distance = 160 meters
(b) Average velocity for the entire journey:
Average velocity is given by the formula:
Average Velocity = Total Distance / Total Time
Substituting the given values:
Average Velocity = 160 meters / 15 seconds
Average Velocity ≈ 10.67 m/s
So, the average velocity for the journey in a straight line is approximately 10.67 m/s.