Question

A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of a = 2.20 m/s2. A worker assists the cart by pushing on the crate with a force that is eastward and has magnitude that depends on time according to f(t) = (5.40 N/s)t. What is the instantaneous power supplied by this force at t = 4.10 s?

Answer 1

To find the instantaneous power supplied by the force at t = 4.10 s, calculate the force using f(t) = (5.40 N/s)t and velocity using Velocity = Initial Velocity + (Acceleration × Time). Then use the equation Power = Force × Velocity to find the instantaneous power.

Step-by-step explanation:

To find the instantaneous power supplied by the force at t = 4.10 s, we need to calculate the force at that time and then use the equation for power:

Power = Force × Velocity

At t = 4.10 s, the force can be found by plugging in the given time into the equation f(t) = (5.40 N/s)t:

f(4.10) = (5.40 N/s)(4.10 s) = 22.14 N

Since the motors in the cart move the crate with a constant eastward acceleration, the velocity at t = 4.10 s can be found using the equation:

Velocity = Initial Velocity + (Acceleration × Time)

Since the crate starts from rest, the initial velocity is 0. Using acceleration a = 2.20 m/s² and time t = 4.10 s, we can calculate the velocity:

Velocity = 0 + (2.20 m/s² × 4.10 s) = 9.02 m/s

Finally, we can calculate the instantaneous power:

Power = (22.14 N) × (9.02 m/s) = 199.69 W