Question

The velocity function (in meters per second) is given for a particle moving along a line.

v(t) = 3t − 7, 0 ≤ t ≤ 4

(a) Find the displacement.

Answer 1

The displacement of the particle is -20 meters.

Step-by-step explanation:

The displacement of a particle can be found by integrating the velocity function with respect to time. In this case, the velocity function is given by v(t) = 3t - 7. To find the displacement, we need to integrate this function over the given time interval of 0 to 4.

Integrating v(t) = 3t - 7 with respect to t gives us s(t) = (3/2)t²- 7t + C, where C is the constant of integration. To find the value of C, we can use the information that the position and velocity are both zero at t = 0.

Plugging in t = 0 and s = 0 into the equation, we get 0 = C. Therefore, the equation for displacement is s(t) = (3/2)t² - 7t.

To find the displacement over the given time interval of 0 to 4, we can substitute t = 4 into the equation and subtract the result when t = 0. This gives us s(4) - s(0) = (3/2)(4²) - 7(4) - [(3/2)(0) - 7(0)] = 8 - 28 = -20 meters.