Question

A particle (P) is moving along a straight line that passes through the fixed point (O). The displacement, (s) metres, of (P) from (O) at time (t) seconds is given by (s=t³-6t²+5t-4) Find the value of (t) for which the acceleration of (P) is (3) m/s²

Answer 1

To find the time at which the acceleration of particle P is 3 m/s², we differentiate the given displacement equation twice to find acceleration and set it equal to 3 m/s², solving for t, which gives us t = 2.5 seconds.

Step-by-step explanation:

The question is asking us to determine the value of t for which the acceleration of particle P is 3 m/s². We are given the displacement-time equation of the particle s = t³ - 6t² + 5t - 4. To find acceleration, we need to differentiate the displacement equation with respect to time twice because acceleration is the second derivative of displacement with respect to time.

Let's find the first derivative which is velocity (v):
v = ds/dt = 3t² - 12t + 5.

Now, we calculate the second derivative which is acceleration (a):
a = dv/dt = d²s/dt² = 6t - 12.

To find the time at which acceleration is 3 m/s², we set the acceleration equation equal to 3 and solve for t:
6t - 12 = 3
6t = 15
t = 2.5 s.

Therefore, the value of t when the acceleration of particle P is 3 m/s² is 2.5 seconds.