Question

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12 + 35 t + 1

Answer 1

The velocity and speed of the particle when t=4 are both 35 m/s since the derivative of the position function s=f(t)=12+35t+1 with respect to time is constant at 35 m/s.

Step-by-step explanation:

The equation of motion for the particle given is s = f(t) = 12 + 35t + 1. To find the velocity at a particular time t, we need to take the derivative of the position function with respect to time to get v(t). For our function, we take the derivative and get:

v(t) = d(12 + 35t + 1)/dt = 35 m/s.

The speed is the absolute value of the velocity and since velocity is constant and positive, speed and velocity are the same at t = 4 s, thus the speed is also 35 m/s.

To summarize, the velocity and speed of the particle when t = 4 are both 35 m/s.

Answer 2

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1

Answer:

Velocity = 131 m/s

Speed = 131 m/s

Step-by-step explanation:

Equation of motion, s = f(t) = 12t² + 35 t + 1

To get velocity of the particle, let us find the first derivative of s

v (t) = ds/dt = 24t + 35

At t = 4

v(4) = 24(4) + 35

v(4) = 131 m/s

Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s