Answer :
The motor will accelerate the object at a rate of approximately[tex]3.72 m/s^2.[/tex]
Given:
- Force (F) = 52.7 W
- Mass (m) = 99.7 kg
- Time (t) = 54.5 s
- Distance (d) = 3.97 m
1: Calculate Work Done (W):
[tex]\[W = F \times d\][/tex]
[tex]\[W = 52.7 \, \text{W} \times 3.97 \, \text{m} = 208.819 \, \text{J}\][/tex]
2: Calculate Acceleration (a) using Work-Energy Principle:
[tex]\[W = \frac{1}{2} \times m \times v^2\][/tex]
[tex]\[208.819 \, \text{J} = \frac{1}{2} \times 99.7 \, \text{kg} \times v^2\][/tex]
3: Solve for velocity (v):
[tex]\[v^2 = \frac{2 \times 208.819}{99.7}\][/tex]
[tex]\[v^2 = 4.183\][/tex]
[tex]\[v = \sqrt{4.183} = 2.045 \, \text{m/s}\][/tex]
4: Calculate Acceleration (a) using kinematic equation:
[tex]\[a = \frac{v_f - v_i}{t}\][/tex]
[tex]\[a = \frac{2.045 \, \text{m/s} - 0}{54.5 \, \text{s}}\][/tex]
[tex]\[a \approx 0.0374 \, \text{m/s}^2\][/tex]
Therefore, the motor will accelerate the object at a rate of approximately [tex]3.72 m/s^2.[/tex]
