A car of mass 800kg attains a speed of 25m/s in 20secs. The power developed in the engine is?
1.25 x 10\(^{4}\)W
2.50x 10\(^{4}\)W
1.25 x 10\(^{6}\)W
2.50 x 10\(^{6}\)W
Explanation
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Power= Energy ÷ time
K.E= ½mv²
Power= [ ½mv²] ÷ t
P= [½×800×25²]÷20
P= [400×625]÷20
P= 250 000 ÷ 20
P=12 500W
P= 1.25×10⁴ W (A)
This two formula are collect but the answers are different when u solve
Ok look at this
Power = work/time
Work = force*distance
Force = mass*acceleration
Acceleration = v-u/t
Noe look at the tricky part
Power= force*distance/time
And distance/time= speed/velocity
So that gives us a new formula to work with
P = fv
F= ma
a= v-u/t
So we are going to have this
P=m(v-u) *v/t
And m=800kg
V= 25m/s
t= 20s
We have
800(25-0)*25/20
25000w/2.5*10^4w✓
So if we use this other formula
P = 1/2mv^2
800*25*25/2*20
12500w /1.25*10^4w and this is in the options
The formula for the kinetic energy is wrong. It's supposed to be 1/2mv∆2 ND not mv∆2 which makes de correct option A.
Power=workdone/time taken
Power=mv^2/t
Power=800×25^2/20
Power=1.25×10^4
Myschool please make corrections
1. Find acceleration: a = Δv / Δt = 25 m/s / 20 s = 1.25 m/s²
2. Find force: F = m × a = 800 kg × 1.25 m/s²
3. Find work done: Work = F × distance = F × 25 m (since distance = speed × time)
4. Find power: Power = Work / time = (F × 25 m) / 20 s
Let's calculate the power
F = 800 kg × 1.25 m/s² = 1000 N
Work = F × distance = 1000 N × 25 m = 25,000 J
Power = Work / time = 25,000 J / 20 s = 1250 W
Converting this to the correct units:
P = 1.25 × 10⁴ W
ass
𝑚
=
800
kg
m=800kg
Final speed
𝑣
=
25
m/s
v=25m/s
Time
𝑡
=
20
s
t=20s
Step 1: Find acceleration
𝑎
=
𝑣
−
𝑢
𝑡
=
25
−
0
20
=
1.25
m/s
2
a=
t
v−u
=
20
25−0
=1.25m/s
2
Step 2: Find force
𝐹
=
𝑚
𝑎
=
800
×
1.25
=
1000
N
F=ma=800×1.25=1000N
Now there are two possible interpretations depending on what your exam expects:
🔹 (A) Power at the final speed
𝑃
=
𝐹
𝑣
=
1000
×
25
=
25,000
W
P=Fv=1000×25=25,000W
🔹 (B) Average power (more commonly expected)
Work done:
𝑊
=
1
2
𝑚
𝑣
2
=
1
2
×
800
×
25
2
=
250,000
J
W=
2
1
mv
2
=
2
1
×800×25
2
=250,000J
Power:
𝑃
=
𝑊
𝑡
=
250,000
20
=
12,500
W
P=
t
W
=
20
250,000
=12,500W
✅ Final Answer (most likely):
Average power = 12,500 W
P= mv²/2t, therefore the answer is supposed to be 1.25×10⁴. cos
P = W/t where W=1/2mv² and then t, by the time we combine this formula the formula should be P= mv²/2t
