Answer:
The policeperson will not be able to catch the speeder in 10 seconds
Explanation:
The maximum acceleration of the 2020 Ford police interceptor, a = 4.4 m/s²
The rate at which the speeding car is moving, v = 70 mph (31.3 m/s)
The time after which the policeperson takes off = 1 second
The time, t, at which the policeperson catches the speeding car is given as follows;
s = u·t + 1/2·a·t²
Where;
u = The initial velocity of the Ford police interceptor = 0
∴ s = 0 × t + 1/2·a·t² = 1/2·a·t²
s = 1/2·a·t²
s = v × (t + 1)
Equating both equations, gives;
v × (t + 1) = 1/2·a·t²
Substituting the values, we get;
31.3 × (t + 1) = 1/2 × 4.4 × t²
31.3·t + 31.3 = 2.2·t²
2.2·t² - 31.3·t - 31.3 = 0
By the quadratic formula, we have;
t = (31.3 ± √((-31.3)² - 4×2.2×(-31.3))/(2 × 2.2)
t ≈ -0.938 seconds or t ≈ 15.165 seconds
The policeperson will catch the speeder in approximately 15.165 seconds
Therefore, the policeperson will not be able to catch the speeder in 10 seconds.
