Question

A particle of mass 0.5 kg is subjected to a force
which varies with distance as shown in graph
F(N)
→X (m)
8 12
If the speed of the particle at x = 0 is 4 m/s, then
its speed at X = 8 m is
(1) 8 m/s
(2) 16 m/s
(3) 32 m/s
(4) 4 m/s​

Answer 1

Answer:

Explanation:

See picture

Answer 2

Given that,

Mass of particle = 0.5 kg

Speed of particle at x = 0 = 4 m/s

According to figure,

We need to calculate the work done during the displacement x = 0 to x =8

Using given figure

Work done = area of triangle+area of square

$W=\dfrac{1}{2}\times4\times10+4\times10$

$W=20+40$

$W=60\ J$

We need to calculate the kinetic energy

Using formula of kinetic energy

$K.E_{i}=\dfrac{1}{2}mv^2$

Put the value into the formula

$K.E_{i}=\dfrac{1}{2}\times0.5\times(4)^2$

$K.E_{i}=4\ J$

We need to calculate the speed of the particle at x = 8

Using work energy theorem

$W=\Delta K.E$

$W=(K.E_{f}-K.E_{i})$

Put the value into the formula

$60=\dfrac{1}{2}\times0.5\times v^2-4$

$64=\dfrac{1}{2}\times0.5\times v^2$

$v^2=\dfrac{2\times64}{0.5}$

$v=\sqrt{\dfrac{2\times64}{0.5}}$

$v=16\ m/s$

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

(2) is correct option

Learn more :

Topic : work energy theorem

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