(a)
First, let's calculate the distance travelled during each stage:
1. Uniform velocity of 12 m/s for 6 seconds:
Distance = velocity x time = 12 m/s x 6s = 72m
2. Acceleration of 2 m/s^2 for 4 seconds:
Initial velocity = 12 m/s
Final velocity = 12 m/s + 2 m/s^2 x 4s = 20 m/s
Average velocity during acceleration = (Initial velocity + Final velocity) / 2 = (12 m/s + 20 m/s) / 2 = 16 m/s
Distance = Average velocity x time = 16 m/s x 4s = 64m
3. Uniform velocity for 2 seconds:
Distance = velocity x time = 20 m/s x 2s = 40m
4. Deceleration to a stop in 15 seconds:
Final velocity = 0 m/s
Initial velocity = 20 m/s (from Stage 2)
Acceleration = (Final velocity - Initial velocity) / time = (0 m/s - 20 m/s) / 15s = -1.33 m/s^2
Distance = Initial velocity x time - (1/2) x acceleration x time^2 = 20 m/s x 15s - (1/2) x (-1.33 m/s^2) x (15s)^2 = 300m + 149.85m = 449.85m
Now, let's calculate the total distance travelled in 5 seconds:
It traveled 6 seconds at 12 m/s, 4 seconds at 16 m/s, and 2 seconds at 20 m/s, so the total distance covered in 5 seconds is:
72m + 64m + 40m + (16 x 1 s) + (20 x 1 s) = 176m
(b)
To calculate the average velocity for the journey, we need to find the total distance traveled and total time taken.
Total distance traveled = 72m + 64m + 40m + 449.85m = 625.85m
Total time taken = 6s + 4s + 2s + 15s = 27s
Average velocity = Total distance / Total time = 625.85m / 27s ≈ 23.18 m/s
Therefore, the average velocity for the journey is 23.18 m/s.
A car moves with uniform velocity of 12 m/s for 6 seconds. It accelerates. 2m / (s ^ 2) for 4 seconds. It then travels for 2 more seconds with uniform velocity. The car finally decelerates to a stop in 15 seconds. Calculate:
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(a) the distance travelled in 5 seconds.
(b) average velocity for the journey, assuming that the journey is in a straight line.
1 answer