Question

"A particle moves along a straight line with the equation of motion s = f(t) = 4t^2 + 6t - 4, where s is measured in meters and t in seconds. Find the velocity when t = 6.

Answer 1

The velocity of the particle at t = 6 seconds is 54 m/s, obtained by differentiating the equation of motion and substituting t = 6 into the velocity function.

Step-by-step explanation:

The student has asked to find the velocity of a particle moving along a straight line with the equation of motion s = f(t) = 4t² + 6t - 4, where s is in meters and t in seconds, at t = 6 seconds. To find the velocity, we need to differentiate the equation of motion with respect to time. The derivative of s with respect to t gives us the velocity function v(t) = ds/dt = 8t + 6. Substituting t = 6 into this velocity function yields v(6) = 8(6) + 6 = 54 m/s.