Step 1 Find Force F as a function of time t.
Force vs. time graph is linear: F = C_{1} t + C_{2}
To evaluate constants C_{1} t + C_{2} :
t = 0, F = 4 gives C_{2} = 4, and
t = 3, F = 0 gives C_{1} = −4/3.
So, F = −(4/3) t + 4.
Step 2 Find velocity v at time t = 4.5 s.
From Newton's 2nd law: F = m dv/dt
Integrating above equation gives
v = (1/m) ∫ F dt = (1/m) [−(4/3) t^{2}/2 + 4 t]
Note v = 0 at t = 0. Substituting m = 2 kg and t = 4.5 s,
v = ½ [−(2/3) (4.5)^{2} + 4 (4.5)] = 2.25 m/s.
Step 3 Find kinetic energy KE at time t = 4.5 s.
KE = ½ m v^{2} = ½ (2) (2.25)^{2} = 5.0625 J.
iit_jee 7 years ago
