A car accelerates from rest at 1.70 m/s2 along a 220-m stretch of road. Find the car’s velocity at the end of the stretch.
d = 0.5at^2,
220 = 0.5 * 1.7 * t^2,
220 = 0.85t^2,
t^2 = 220 / 0.85 = 258.8,
t = sqrt(258.8) = 16.1 m.
V = at,
= 1.7 * 16.1 = 27.3 m/s.
CORRECTION:t = sqrt(258.8) = 16.1 s.
To find the car's velocity at the end of the stretch, you need to use the equation of motion for uniformly accelerated motion:
v^2 = u^2 + 2aS
Where:
- v is the final velocity
- u is the initial velocity (in this case, the car starts from rest, so u = 0)
- a is the acceleration
- S is the distance traveled
In this case, u = 0 m/s, a = 1.70 m/s^2, and S = 220 m. Plugging these values into the equation, we get:
v^2 = 0^2 + 2 * 1.70 * 220
v^2 = 0 + 748
v^2 = 748
To find the velocity at the end of the stretch, we need to find v. Taking the square root of both sides:
v = sqrt(748)
Using a calculator, we find:
v ≈ 27.36 m/s
Therefore, the car's velocity at the end of the stretch is approximately 27.36 m/s.