A body of mass 1 kg begins to move under the action of a time dependent force F-2t-3t2-N- where - and - are unit vectors along x and y axis- What power will be developed by the force at the time t-

The correct option is D (2t^3+3t^5)W Applying Newton's second #160;law of motion, acceleration, a⃗=F⃗m=2t î + 3t^2 ĵ Acceleration is defined as ra ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Second Law of Motion

A body of mas...

Question

A body of mass $1$ kg begins to move under the action of a time dependent force $\to F = (2 t^i + 3 t^{2}^j) N,$ where $^i$ and $^j$ are unit vectors along x and y axis. What power will be developed by the force at the time $t$ ?

(2 t^{2} + 3 t^{3}) W

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

(2 t^{2} + 4 t^{4}) W

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

(2 t^{3} + 3 t^{4}) W

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

(2 t^{3} + 3 t^{5}) W

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

Open in App

Solution

The correct option is D $(2 t^{3} + 3 t^{5}) W$
Applying Newton's second law of motion, acceleration, $\to a = \frac{\to F}{m} = 2 t^i + 3 t^{2}^j$

Acceleration is defined as rate of change of velocity,
$\to a = \frac{d \to v}{d t}$
$\to v = \int_{0}^{t} \to a d t$
$\to v = \int_{0}^{t} (2 t^i + 3 t^{2}^j) d t$
$\to v = t^{2}^i + t^{3}^j$

Power, $P = \to F . \to v = (2 t^i + 3 t^{2}^j) . (t^{2}^i + t^{3}^j)$
$P = (2 t^{3} + 3 t^{5}) W$

Suggest Corrections

Similar questions

Q. A body of mass

1 kg

begins to move under the action of a time dependent force

\to F = (2 t^i + 3 t^{2}^j) N

, where

^i

and

^j

are the unit vectors along the

x

and

y

axis. What power will be developed by the force at the time

t

Q. A body of mass

1 kg

begins to move under the action of a time dependent force

\to F = (2 t^i + 3 t^{2}^j) N

. Calculate the instantaneous power developed at time

t

Q. A body of mass

1 kg

begins to move under the action of a time dependent force

\to F = (2 t^i + 3 t^{2}^j) N

. Calculate the instantaneous power developed at time

t

Q. At

t = 0

, a particle starts from

(- 2, 0)

and moves towards positive

x -

axis with speed of

v = 6 t^{2} + 4 t m/s

. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

Q. A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F = -

^i

+ 2

^j

+ 3

^k

N where

^i

^j

^k

are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?

Join BYJU'S Learning Program

A body of mass 1 kg begins to move under the action of a time dependent force →F=(2t^i+3t2^j)N, where ^i and ^j are unit vectors along x and y axis. What power will be developed by the force at the time t?

The correct option is D (2t3+3t5)WApplying Newton's second law of motion, acceleration, →a=→Fm=2t^i+3t2^jAcceleration is defined as rate of change of velocity,→a=d→vdt→v=∫t0→adt→v=∫t0(2t^i+3t2^j)dt→v=t2^i+t3^jPower, P=→F.→v=(2t^i+3t2^j).(t2^i+t3^j)P=(2t3+3t5) W

A body of mass $1$ kg begins to move under the action of a time dependent force $\to F = (2 t^i + 3 t^{2}^j) N,$ where $^i$ and $^j$ are unit vectors along x and y axis. What power will be developed by the force at the time $t$ ?