Answer:
The value of c is 27.4 m/s²
Explanation:
Hi there!
Let´s write the position function:
x = 3.0 m + (4.0 m/s) · t + c · t² - (1.6 m/s³) · t³
The velocity of the particle is given by the derivative of the position function with respect to time:
dx/dt = v = 4.0 m/s + 2 · c · t - 4.8 m/s³ · t²
The acceleration of the particle is the derivative of the velocity function with respect to t:
dv/dt = a = 2 · c - 9.6 m/s³ · t
The applied force at t = 3.0 s is calculated as follows:
F = m · a
Where:
F = applied force.
m = mass of the particle.
a = acceleration.
Then:
F = m · a
36 N = 1.4 kg · a
36 N / 1.4 kg = a
a = 26 m/s²
We have derived the equation of the acceleration above:
a = 2 · c - 9.6 m/s³ · t
Then, using a = 26 m/s² and t = 3.0 s, we can solve the equation for c:
26 m/s² = 2 · c - 9.6 m/s³ · 3.0 s
26 m/s² + 9.6 m/s³ · 3.0 s = 2 · c
54.8 m/s² = 2 · c
54.8 m/s² / 2 = c
c = 27.4 m/s²
The value of c is 27.4 m/s²
