If a #2 kg# object is being constantly accelerated from #0m/s# to #15 m/s# over # 6s#, how much power is being applied at #t= 3 #?

Question

If a #2 kg# object is being constantly accelerated from #0m/s# to #15 m/s# over # 6s#, how much power is being applied at #t= 3   #?

Charles Aeschliman · Accepted Answer

P = 19 W

To solve this problem we will first find the value of acceleration involved, then use that to determine the resultant force required to produce that acceleration, then find the velocity at 3 s, and lastly calculate the power. The object has a constant acceleration so the force is constant and the equations of uniform acceleration can be used. 1. Calculate the acceleration. #s =?# #u = 0# #v = 15 m.s^(-1)# #a =?# #t = 6 s # Use #v = u + at ⇒ a = (v-u)/t# #⇒ a = (15-0)/6= 2.5 m.s^(-2)# 2. Resultant force. #F=ma = 2× 2.5 = 5.0 N# 3. Velocity at 3 s. We can use an equation of constant acceleration to determine the velocity of the object at 3 seconds. #v= u + at = 0 + 2.5 × 3 = 7.5 m s^(-1)# 4. Power. #P = Fv = 5.0 × 7.5 = 37.5 = 38 W# (2 sf)

Adrian Ayala · Answer

undefined To find the power at t = 3s, first, calculate the acceleration using the formula $ a = \frac{v - u}{t} $, where $ v $ is the final velocity, $ u $ is the initial velocity, and $ t $ is the time taken. Then, use the formula $ P = F \cdot v $, where $ P $ is power, $ F $ is force, and $ v $ is velocity. Finally, substitute $ P = F \cdot v $ into $ P = m \cdot a $ to find the power.