Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Momentum P of a Particle Changes with Time T According to the Relation D P D T = ( 10 N ) + ( 2 N / S ) T If the Momentum is Zero at T = 0, What Will the Momentum Be at T = 10 - Physics

Sum

The momentum p of a particle changes with time t according to the relation
$\frac{dp}{dt} = \left( 10 N \right) + \left( 2 N/s \right)t$ If the momentum is zero at t = 0, what will the momentum be at t = 10 s?

#### Solution

According to the question, we have:
$\frac{dp}{dt} = \left( 10 N \right) + \left( 2 N/s \right)t$
Momentum is zero at time, t = 0
Now, dp = [(10 N) + (2 Ns−1)t]dt

On integrating the above equation, we get:
$p = \int_0^{10} dp = \int_0^{10} 10 dt + \int_0^{10} \left( 2t dt \right)$
$\Rightarrow p = \left[ 10t + 2\frac{t^2}{2} \right]_0^{10}$
$\Rightarrow p = 10 \times 10 + 100 - 0$
$\therefore p = 100 + 100 = 200 \text{ kg } m/s$

Concept: Scope and Excitement of Physics
Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 28 | Page 30

Share