A car of mass 800kg attains a speed of 25m/s in 20 secs. The power developed in the engine is
1 . 25 x 104 W
2 . 50 x 104 W
1 . 25 x 106W
2 . 50 x 106 W
Explanation
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Wrong... D ryt tin is power=force x velocity... Force=ma...
Therefore a=v/t... A=25/20=1.25...
Power=800x1.25x25=25000 or 2.5x10^4watts
power =work/time=energy/time ,since velocity z given without height i use P=k.E/time . . p=(mv^2)/2 -: t . . .subtituting, P=(800*25*25)/2 :- 20 ,P=500000/2 :- 20 ,P=500000/2 * 1/20 =1.25 *10^4 W or J/s
My answer to this question is option A
I solved it using 2 methods and arrived at the same answer.
Method 1
Using power = m(V² - U²/2t)
P= 800(25² - 0²/2x20)
P=800(25²/40)
P=12500
P=1.25x10⁴ W
Method 2
M=800, V=25, t=20
Using v=u+at to find acceleration a
25= 0 + ax20
a = 25/20
a =1.25ms¯²
Recall power = workdone/Time taken
And workdone = fxd
So p= fxd/t
Also recall force= m X a
So Power = M X a X d / t
To find the distance d we use; V² =U² +2as
25² = 0² + 2 x 1.25 x S
S = 25²/2x1.25
S = 250m
Now we have a=1.25; S (distance) = 250m
Substitute these values into;
P = M x a x d /t
P = 800 X 1.25 X 250 / 20
P = 12500w
P = 1.25x10⁴ W
M= 800kg
V=25m/s
T=20sec....
P= ?
Therefore P= w/T buh no height is specify so P=E/T where E= 1/2*mv2 so i substitute in {1/2* mv2} / {T}
{1/2 * 400*25*25} / {20} = 1.25*10^4W
From the question,
M= 800kg
V= 25m/s
T= 20sec
P= ?
Power = work/time
work is "mgh" since we are not given height in the question we make use of (1/2) x mv^2
P= (mv^2)/2T
-: (800x25x25)/(2x20)
P= 12500watt or 1.25x 10^4watt
IT IS WELL
M-800KG
V-25MS-¹
T-20SECS
FIRST CALCULATE K.E : 1/2MV²
0.5×800×25²
0.5×800×625
250,000J
POWER DEVELOPED (P): WORK DONE/TIME
250000/20 = 12500W OR 1.25×10⁴
YOU GET IT NOW???
Mass = 800kg
Final velocity, v = 25m/s
Initial velocity, u =0
Time =20s
Formula 1
*Calculate the workdone
The work done is equal to kinetic energy
KE =1 /2 mv²
=1 /2×800 ×(25)²
= 250000 Joules
* Calculate power
Power =Workdone /Time
=250000 /20 =12500 W
= 1.25×10⁴ W
Formula 2
*Calculate the acceleration
a = v-u/t
= 25-0/20 = 1.25 m/s²
*Calculate the force
F= ma
=800 × 1.25= 1000N
*Calculate the average velocity
v_avg = u+v/2
v_avg = (0 m/s + 25 m/s) / 2 = 12.5 m/s
Why am I using average velocity instead of the final velocity (25m/s): It is because Average Velocity is More Accurate. When calculating power using the formula P = F × v, the velocity (v) should represent the velocity over the time period during which the force (F) is applied.
In this case, the car accelerates from rest to 25 m/s over a period of 20 seconds. The force (F) is applied over this entire 20-second period, not just at the instant when the car reaches 25 m/s. Using the final velocity (25 m/s) would assume that the force (F) is applied only at that instant, which isn't accurate. The force is applied over the entire 20-second period, during which the velocity is changing.
*Average Velocity Represents the Velocity Over the Time Period*
The average velocity (v_avg), on the other hand, represents the velocity over the entire time period during which the force (F) is applied. Using the average velocity (12.5 m/s) provides a more accurate representation of the velocity over the 20-second period during which the force (F) is applied.
*Calculate the power
Power = Force × Velocity
= 1000 × 12.5 = 12500 W
=1.25 × 10⁴ W
Here is an explanation:
Power = Force x distancetime = m(v−u)t×v
800(25−0)20×25 = 2.5 x 10 4 watts
All lies the answer is B...P=fv. a=v/t v=25 t=20 a=1.25 F=ma m=800 therefore F=800*1.25=1000 Power=1000*25=25000 =2.5*10^4
The crt. ans is B
here is how I came about it
Power=Work done/time
Workdone=Force x distance
Force= mass x acceleration
acceleration= velocity/time
and
distance= speed x time, because speed= distance/time
now, putting all this formula together we have:
Power= Work done/time mass=800kg, velocity=25m/s
=Force x distance/time time=20secs, speed=25m/s
=mass x acceleration/time Note Speed and Velocity are
=mass x velocity/time x distance/time the same.
=mass x velocity/time x speed x time/time
Power=800(25/20) x 25 x 20/20
=800(1.25) x 25 x 20/20
=1,000 x 25 x 20/20
=25,000 x 20/20
=500,000/20
=25,000
=2.5 x 10^4
m=800kg,final speed=25m/s,initial speed=0. p=w/t,workdone=change in K.E=1/2MV^2-1/2MV^2
W=1/2mv^2=1/2.800.25^2=250000J
P=W/T=250000/20=12500W
power= work/ time. But work=mah . Therefore, power=mah/t and h=vt which is power=mavt/t, t will cancel out leaving mav. Recall, a=v/t. Substituting we have, power=mvv/t which is also mv^2/t.
m=800kg, v=25m/s and t=20sec
Using the formula mv^2/t, Power=800*25*25/20 . P=25000 or 25 *10^4watts
P=W/t................................eqn 1
Note:
W = F x s
= ma x s
= m(v/t) x h
W = mvh/t .................... eqn 2
put eqn 2 in eqn 1, we have
P = mvh / t²
since h was not given and we know h/t=v, therefore P will be deduced further to be
P = mv² / t.........................( substitute the given values of m , v and t.
See you next class...
