Question

a particle of mass 0.5 kg is subjected to a force which varies with distance as shown in graph if the spedd of the particle atx=0 is 4m/s then its speed at x=8m is​

Answer 1

Answer:

16m/s

hint .

area under graph is equal to the change in kinetic energy

Answer 2

Answer:

The speed of the particle at 8 m is 16 m/s.

Explanation:

Given that,

Mass of particle = 0.5 kg

Speed of the particle at x = 0 is 4 m/s.

We need to calculate the speed at x = 8 m

Area under the curve x = 0 to x = 8.

It is a shape of trapezium.

It is force vs displacement graph

Therefore, are under the curve gives work done by a particle

Work done = change in kinetic energy

Area of trapezium = change in kinetic energy

$\dfrac{1}{2}\times H(b_{1}+b_{2})=\dfrac{1}{2}mv_{f}^2 -\dfrac{1}{2}mv_{i}^2$

Put the value into the formula

$\dfrac{1}{2}\times10(4+8)=\dfrac{1}{2}\times0.5(v_{f}^2-4^2)$

$\dfrac{60\times2}{0.5}+16=v_{f}^2$

$v_{f}=\sqrt{256}$

$v_{f}=16\ m/s$

Hence, The speed of the particle at 8 m is 16 m/s.