Answer:
Magnitude of velocity when s is 10 m= 4.58m/s
Magnitude of acceleration when s is 10 m = 0.653 m/s²
Explanation:
Radius of circular path = 50m
Speed = 4m/s
increase in acceleration = (0.05s)m/s²
speed and acceleration when s is 10 m = ?
Magnitude of Velocity:
From third equation of motion
[tex]v_{f}^{2}-v_{i}^{2}=2aS\\\\v_{f}=\sqrt{2aS+v_{i}^{2}} \\\\v_{f}=\sqrt{2(0.05)(10)+(4)^{2}} \\\\v_{f}=4.58\,m/s[/tex]
Magnitude of Acceleration:
[tex]a=\sqrt{a_{t}^{2}+a_{n}^{2}}--(1)[/tex]
The tangential component of acceleration is
[tex]a_{t}=(0.05)(10)\\a_{t}=0.5\,m/s^{2}[/tex]
The normal component of acceleration is
[tex]a_{n}=\frac{v^{2}}{R}\\\\a_{n}=\frac{16}{50}\\\\a_{n}=0.42\,m/s^{2}[/tex]
Substituting tangential and normal component in (1)
[tex]a=\sqrt{(0.5)^{2} +(0.42)^{2} }[/tex]
a=0.653 m/s²
