Answer:
U = 30 m/s
a = 3 m/s²
Explanation:
"A car accelerating uniformly from rest reaches a maximum speed of U in 10 s. It then moves with that speed for an additional 20 s. The distance covered by the car in the 30 s interval is 750 m. Find U and the acceleration of the car in the first 10 s."
During the first 10 s:
v₀ = 0 m/s
v = U m/s
t = 10 s
The distance covered in this time is the average velocity times time:
Δx = ½ (v + v₀) t
Δx = ½ (U + 0) (10)
Δx = 5U
The distance covered in the next 20 seconds is speed times time:
Δx = 20U
The total distance is 750 m:
5U + 20U = 750
25U = 750
U = 30 m/s
The acceleration during the first 10 seconds is the change in speed over change in time.
a = Δv / Δt
a = (30 m/s − 0 m/s) / 10 s
a = 3 m/s²
