Question

a cart of mass ( m = 4 \text{ kg} ) slides along a horizontal surface with an initial velocity of ( 5 \text{ m/s} ). a net force of ( 8 \text{ n} ) is then exerted on the cart in the direction of motion for ( 3 \text{ s} ). what is the average power delivered to the cart during the three seconds the force is applied?

a ( 24 \text{ w} )
b ( 40 \text{ w} )
c ( 64 \text{ w} )
d ( 88 \text{ w} )

Explanation:

Step1: Calculate acceleration

Using Newton's second law \(F = ma\), where \(F = 8\space N\) and \(m = 4\space kg\).

$$a=\frac{F}{m}=\frac{8}{4}=2\space m/s^{2}$$

Step2: Calculate final velocity

Using the kinematic equation \(v = u+at\), where \(u = 5\space m/s\), \(a = 2\space m/s^{2}\) and \(t = 3\space s\)

$$v=5 + 2\times3=11\space m/s$$

Step3: Calculate average velocity

The formula for average velocity \(\bar{v}=\frac{u + v}{2}\)

$$\bar{v}=\frac{5+11}{2}=8\space m/s$$

Step4: Calculate average power

The formula for average power \(P = F\bar{v}\), where \(F = 8\space N\) and \(\bar{v}=8\space m/s\)

$$P=8\times8 = 64\space W$$

Answer:

C. \(64\space W\)