A force 2 -3 -k- N acting on a body- displaces it from r1-2 -3 k- m to r2-8 t2-9 t3-7 t k- m- Find the instantaneous power delivered by the force at t -1 sec-A- 100 WB- 60 WC- 80 WD- 120 W

Displacement vector is given by S=r_2 r_1 =(8t^2î+9t^3ĵ+7tk̂) (2î+ĵ+3k̂) =(8t^2 2)î+(9t^3 1)ĵ+(7t 3)k̂ m Work done by the force F is given by W=F.S =(2î+3ĵ+k̂). ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Average and Instaneous Power

A force 2 î+3...

Question

A force $(2^i + 3^j +^k) N$ acting on a body, displaces it from $_{1} = (2^i +^j + 3^k) m$ to $_{2} = (8 t^{2}^i + 9 t^{3}^j + 7 t^k) m$ . Find the instantaneous power delivered by the force at $t = 1 sec$ .

100 W

No worries! We‘ve got your back. Try BYJU‘S free classes today!

60 W

No worries! We‘ve got your back. Try BYJU‘S free classes today!

80 W

No worries! We‘ve got your back. Try BYJU‘S free classes today!

120 W

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $120 W$
Displacement vector is given by $\to S =_{2} -_{1}$
$= (8 t^{2}^i + 9 t^{3}^j + 7 t^k) - (2^i +^j + 3^k)$
$= (8 t^{2} - 2)^i + (9 t^{3} - 1)^j + (7 t - 3)^k m$
Work done by the force $\to F$ is given by
$W = \to F . \to S$
$= (2^i + 3^j +^k) . [(8 t^{2} - 2)^i + (9 t^{3} - 1)^j + (7 t - 3)^k)]$
$= (16 t^{2} - 4) + (27 t^{3} - 3) + (7 t - 3)$
$W = (27 t^{3} + 16 t^{2} + 7 t - 10) J$

Instantaneous power is given by, $P = \frac{d W}{d t}$
$\Rightarrow P = \frac{d}{d t} (27 t^{3} + 16 t^{2} + 7 t - 10) = 81 t^{2} + 32 t + 7$

$∴$ Instantaneous power at $t = 1 sec$ is given by $P_{t = 1 sec} = 81 \times (1)^{2} + 32 \times (1) + 7$
$= 81 + 32 + 7$
$= 120 W$

Suggest Corrections

Similar questions

Q. A force

(2^i + 3^j +^k) N

acting on a body, displaces it from

_{1} = (2^i +^j + 3^k) m

_{2} = (8 t^{2}^i + 9 t^{3}^j + 7 t^k) m

. Find the instantaneous power delivered by the force at

t = 1 sec

Q. A force

(4^i +^j - 2^k) N

acting on a body maintains its velocity at

(2^i + 2^j + 3^k) m s^{- 1}

. The power exerted is:

Q. A constant force

\to F = 2^i - 3^j +^k

is applied on a ball to displace it from

_{1} =^i +^j

_{2} = 4^i + 3^j

, which of the following statements is true?

Q. A body initially at rest has an acceleration of

10^j m / s^{2}

. If the force acting on the body is

\to F = (2^i + 3^j + 5^k) N

, the instantaneous power at

t = 5

s will be:

Q. A force

(4^i +^j - 2^k) N

acting on a body maintains its velocity at

(2^i + 3^j -^k) m/s

. The power exerted is

Join BYJU'S Learning Program

Explore more

Average and Instaneous Power

Standard XII Physics

Join BYJU'S Learning Program

A force (2^i+3^j+^k) N acting on a body, displaces it from →r1=(2^i+^j+3^k) m to →r2=(8t2^i+9t3^j+7t^k) m. Find the instantaneous power delivered by the force at t=1 sec.

A force $(2^i + 3^j +^k) N$ acting on a body, displaces it from $_{1} = (2^i +^j + 3^k) m$ to $_{2} = (8 t^{2}^i + 9 t^{3}^j + 7 t^k) m$ . Find the instantaneous power delivered by the force at $t = 1 sec$ .