To determine the instantaneous velocity and acceleration of the body, we need to perform the following steps, assuming that 'PT squared' refers to 'P times T squared', where P is a constant and T is time:

1. Define the displacement equation:

Given: Displacement, s(t) = PT² + 40T + 7

2. Calculate the instantaneous velocity:

Instantaneous velocity, v(t), is the first derivative of displacement with respect to time (T).

v(t) = ds/dt = d(PT² + 40T + 7)/dt

v(t) = 2PT + 40

3. Calculate the instantaneous acceleration:

Instantaneous acceleration, a(t), is the first derivative of velocity with respect to time (T), or the second derivative of displacement with respect to time.

a(t) = dv/dt = d(2PT + 40)/dt

a(t) = 2P

Therefore:

• Instantaneous Velocity: v(t) = 2PT + 40
• Instantaneous Acceleration: a(t) = 2P